# Ejercicio 285

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CAPITULO XXXVI

Ejercicio 285
Transformar en suma algebraica de radicales simples:
1. $\begin{array}{cc}\sqrt{5+\sqrt{24}}& \\ & \\ & Sea:\\ & \\ & a=5\\ & b=24\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{5}^{2}–24}\\ m& =\sqrt{25–24}\\ m& =\sqrt{1}\\ m& =1\\ & \\ \sqrt{5+\sqrt{24}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{5+1}{2}}+\sqrt{\frac{5–1}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{3}+\sqrt{2}\end{array}$
2. $\begin{array}{cc}\sqrt{8–\sqrt{60}}& \\ & \\ & Sea:\\ & \\ & a=8\\ & b=60\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{8}^{2}–60}\\ m& =\sqrt{64–60}\\ m& =\sqrt{4}\\ m& =2\\ & \\ \sqrt{8–\sqrt{60}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{8+2}{2}}–\sqrt{\frac{8–2}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{5}–\sqrt{3}\end{array}$
3. $\begin{array}{cc}\sqrt{8+\sqrt{28}}& \\ & \\ & Sea:\\ & \\ & a=8\\ & b=28\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{8}^{2}–28}\\ m& =\sqrt{64–28}\\ m& =\sqrt{36}\\ m& =6\\ & \\ \sqrt{8+\sqrt{28}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{8+6}{2}}+\sqrt{\frac{8–6}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{\overline{)2}}{\overline{)2}}}\\ & =\sqrt{7}+1\end{array}$
4. $\begin{array}{cc}\sqrt{32–\sqrt{700}}& \\ & \\ & Sea:\\ & \\ & a=32\\ & b=700\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{3{2}^{2}–700}\\ m& =\sqrt{1024–700}\\ m& =\sqrt{324}\\ m& =18\\ & \\ \sqrt{32–\sqrt{700}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{32+18}{2}}–\sqrt{\frac{32–18}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =5–\sqrt{7}\end{array}$
5. $\begin{array}{cc}\sqrt{14+\sqrt{132}}& \\ & \\ & Sea:\\ & \\ & a=14\\ & b=132\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{1{4}^{2}–132}\\ m& =\sqrt{196–132}\\ m& =\sqrt{64}\\ m& =8\\ & \\ \sqrt{14+\sqrt{132}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{14+8}{2}}+\sqrt{\frac{14–8}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{11}+\sqrt{3}\end{array}$
6. $\begin{array}{cc}\sqrt{13+\sqrt{88}}& \\ & \\ & Sea:\\ & \\ & a=13\\ & b=88\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{1{3}^{2}–88}\\ m& =\sqrt{169–88}\\ m& =\sqrt{81}\\ m& =9\\ & \\ \sqrt{13+\sqrt{88}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{13+9}{2}}+\sqrt{\frac{13–9}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{11}+\sqrt{2}\end{array}$
7. $\begin{array}{cc}\sqrt{11+2\sqrt{30}}& =\sqrt{11+\sqrt{120}}\\ & \\ & Sea:\\ & \\ & a=11\\ & b=120\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{1{1}^{2}–120}\\ m& =\sqrt{121–120}\\ m& =\sqrt{1}\\ m& =1\\ & \\ \sqrt{11+2\sqrt{30}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{11+1}{2}}+\sqrt{\frac{11–1}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{6}+\sqrt{5}\end{array}$
8. $\begin{array}{cc}\sqrt{84–18\sqrt{3}}& =\sqrt{84–\sqrt{972}}\\ & \\ & Sea:\\ & \\ & a=84\\ & b=972\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{8{4}^{2}–972}\\ m& =\sqrt{7056–972}\\ m& =\sqrt{6084}\\ m& =78\\ & \\ \sqrt{84–18\sqrt{3}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{84+78}{2}}–\sqrt{\frac{84–78}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =9–\sqrt{3}\end{array}$
9. $\begin{array}{cc}\sqrt{21+6\sqrt{10}}& =\sqrt{21+\sqrt{360}}\\ & \\ & Sea:\\ & \\ & a=21\\ & b=360\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{2{1}^{2}–360}\\ m& =\sqrt{441–360}\\ m& =\sqrt{81}\\ m& =9\\ & \\ \sqrt{21+6\sqrt{10}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{21+9}{2}}+\sqrt{\frac{21–9}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{15}+\sqrt{6}\end{array}$
10. $\begin{array}{cc}\sqrt{28+14\sqrt{3}}& =\sqrt{28+\sqrt{588}}\\ & \\ & Sea:\\ & \\ & a=28\\ & b=588\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{2{8}^{2}–588}\\ m& =\sqrt{784–588}\\ m& =\sqrt{196}\\ m& =14\\ & \\ \sqrt{28+14\sqrt{3}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{28+14}{2}}+\sqrt{\frac{28–14}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{21}+\sqrt{7}\end{array}$
11. $\begin{array}{cc}\sqrt{14–4\sqrt{6}}& =\sqrt{14–\sqrt{96}}\\ & \\ & Sea:\\ & \\ & a=14\\ & b=96\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{1{4}^{2}–96}\\ m& =\sqrt{196–96}\\ m& =\sqrt{100}\\ m& =10\\ & \\ \sqrt{14–4\sqrt{6}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{14+10}{2}}–\sqrt{\frac{14–10}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{12}–\sqrt{2}\\ & =2\sqrt{3}–\sqrt{2}\end{array}$
12. $\begin{array}{cc}\sqrt{55+30\sqrt{2}}& =\sqrt{55+\sqrt{1800}}\\ & \\ & Sea:\\ & \\ & a=55\\ & b=1800\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{5{5}^{2}–1800}\\ m& =\sqrt{3025–1800}\\ m& =\sqrt{1225}\\ m& =35\\ & \\ \sqrt{55+30\sqrt{2}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{55+35}{2}}+\sqrt{\frac{55–35}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{45}+\sqrt{10}\\ & =\sqrt{5.{3}^{2}}+\sqrt{10}\\ & =3\sqrt{5}+\sqrt{10}\end{array}$
13. $\begin{array}{cc}\sqrt{73–12\sqrt{35}}& =\sqrt{73–\sqrt{5040}}\\ & \\ & Sea:\\ & \\ & a=73\\ & b=5040\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{7{3}^{2}–5040}\\ m& =\sqrt{5329–5040}\\ m& =\sqrt{289}\\ m& =17\\ & \\ \sqrt{73–12\sqrt{35}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{73+17}{2}}–\sqrt{\frac{73–17}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{45}–\sqrt{28}\\ & =\sqrt{5.{3}^{2}}–\sqrt{7.{2}^{2}}\\ & =3\sqrt{5}–2\sqrt{7}\end{array}$
14. $\begin{array}{cc}\sqrt{253–60\sqrt{7}}& =\sqrt{253–\sqrt{25200}}\\ & \\ & Sea:\\ & \\ & a=253\\ & b=25200\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{25{3}^{2}–25200}\\ m& =\sqrt{64009–25200}\\ m& =\sqrt{38809}\\ m& =197\\ & \\ \sqrt{253–60\sqrt{7}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{253+197}{2}}–\sqrt{\frac{253–197}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =15–\sqrt{28}\\ & =15–\sqrt{7.{2}^{2}}\\ & =15–2\sqrt{7}\end{array}$
15. $\begin{array}{cc}\sqrt{293–30\sqrt{22}}& =\sqrt{293–\sqrt{19800}}\\ & \\ & Sea:\\ & \\ & a=293\\ & b=19800\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{29{3}^{2}–19800}\\ m& =\sqrt{85849–19800}\\ m& =\sqrt{66049}\\ m& =257\\ & \\ \sqrt{293–30\sqrt{22}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{293+257}{2}}–\sqrt{\frac{293–257}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{275}–\sqrt{18}\\ & =\sqrt{11.{5}^{2}}–\sqrt{2.{3}^{2}}\\ & =5\sqrt{11}–3\sqrt{2}\end{array}$
16. $\begin{array}{cc}\sqrt{\frac{5}{6}+\sqrt{\frac{2}{3}}}& \\ & \\ & Sea:\\ & \\ & a=\frac{5}{6}\\ & b=\frac{2}{3}\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{\left(\frac{5}{6}\right)}^{2}–\frac{2}{3}}\\ m& =\sqrt{\frac{25}{36}–\frac{2}{3}}\\ m& =\sqrt{\frac{1}{36}}\\ m& =\frac{1}{6}\\ & \\ \sqrt{\frac{5}{6}+\sqrt{\frac{2}{3}}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{\frac{5}{6}+\frac{1}{6}}{2}}+\sqrt{\frac{\frac{5}{6}–\frac{1}{6}}{2}}\\ & =\sqrt{\frac{1}{2}}+\sqrt{\frac{\frac{\overline{)4}}{}}{\overline{)2}}}\\ & =\sqrt{\frac{1}{2}}+\sqrt{\frac{1}{3}}\\ & =\frac{\sqrt{1}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}+\frac{\sqrt{1}}{\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}}\\ & =\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}\end{array}$
17. $\begin{array}{cc}\sqrt{\frac{3}{4}–\sqrt{\frac{1}{2}}}& \\ & \\ & Sea:\\ & \\ & a=\frac{3}{4}\\ & b=\frac{1}{2}\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{\left(\frac{3}{4}\right)}^{2}–\frac{1}{2}}\\ m& =\sqrt{\frac{9}{16}–\frac{1}{2}}\\ m& =\sqrt{\frac{1}{16}}\\ m& =\frac{1}{4}\\ & \\ \sqrt{\frac{3}{4}–\sqrt{\frac{1}{2}}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{\frac{3}{4}+\frac{1}{4}}{2}}–\sqrt{\frac{\frac{3}{4}–\frac{1}{4}}{2}}\\ & =\sqrt{\frac{1}{2}}–\sqrt{\frac{\frac{1}{2}}{2}}\\ & =\sqrt{\frac{1}{2}}–\sqrt{\frac{1}{4}}\\ & =\frac{\sqrt{1}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}–\frac{1}{2}\\ & =\frac{\sqrt{2}}{2}–\frac{1}{2}\\ & =\frac{1}{2}\left(\sqrt{2}–1\right)\end{array}$
18. $\begin{array}{cc}\sqrt{\frac{9}{16}+\sqrt{\frac{1}{8}}}& \\ & \\ & Sea:\\ & \\ & a=\frac{9}{16}\\ & b=\frac{1}{8}\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{\left(\frac{9}{16}\right)}^{2}–\frac{1}{8}}\\ m& =\sqrt{\frac{81}{256}–\frac{1}{8}}\\ m& =\sqrt{\frac{49}{256}}\\ m& =\frac{7}{16}\\ & \\ \sqrt{\frac{9}{16}+\sqrt{\frac{1}{8}}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{\frac{9}{16}+\frac{7}{16}}{2}}+\sqrt{\frac{\frac{9}{16}–\frac{7}{16}}{2}}\\ & =\sqrt{\frac{1}{2}}+\sqrt{\frac{\frac{1}{8}}{2}}\\ & =\sqrt{\frac{1}{2}}+\sqrt{\frac{1}{16}}\\ & =\frac{\sqrt{1}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}+\frac{1}{4}\\ & =\frac{\sqrt{2}}{2}+\frac{1}{4}\end{array}$
19. $\begin{array}{cc}6+4\sqrt{2}& \\ & \\ \sqrt{6+4\sqrt{2}}& =\sqrt{6+\sqrt{32}}\\ & \\ & Sea:\\ & \\ & a=6\\ & b=32\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{6}^{2}–32}\\ m& =\sqrt{36–32}\\ m& =\sqrt{4}\\ m& =2\\ & \\ \sqrt{6+4\sqrt{2}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{6+2}{2}}+\sqrt{\frac{6–2}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =2+\sqrt{2}\end{array}$
20. $\begin{array}{cc}7+4\sqrt{3}& \\ & \\ \sqrt{7+4\sqrt{3}}& =\sqrt{7+\sqrt{48}}\\ & \\ & Sea:\\ & \\ & a=7\\ & b=48\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{7}^{2}–48}\\ m& =\sqrt{49–48}\\ m& =\sqrt{1}\\ m& =1\\ & \\ \sqrt{7+4\sqrt{3}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{7+1}{2}}+\sqrt{\frac{7–1}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =2+\sqrt{3}\end{array}$
21. $\begin{array}{cc}8+2\sqrt{7}& \\ & \\ \sqrt{8+2\sqrt{7}}& =\sqrt{8+\sqrt{28}}\\ & \\ & Sea:\\ & \\ & a=8\\ & b=28\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{8}^{2}–28}\\ m& =\sqrt{64–28}\\ m& =\sqrt{36}\\ m& =6\\ & \\ \sqrt{8+2\sqrt{7}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{8+6}{2}}+\sqrt{\frac{8–6}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{\overline{)2}}{\overline{)2}}}\\ & =\sqrt{7}+1\end{array}$
22. $\begin{array}{cc}10+2\sqrt{21}& \\ & \\ \sqrt{10+2\sqrt{21}}& =\sqrt{10+\sqrt{84}}\\ & \\ & Sea:\\ & \\ & a=10\\ & b=84\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{1{0}^{2}–84}\\ m& =\sqrt{100–84}\\ m& =\sqrt{16}\\ m& =4\\ & \\ \sqrt{10+2\sqrt{21}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{10+4}{2}}+\sqrt{\frac{10–4}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{7}+\sqrt{3}\end{array}$
23. $\begin{array}{cc}18+6\sqrt{5}& \\ & \\ \sqrt{18+6\sqrt{5}}& =\sqrt{18+\sqrt{180}}\\ & \\ & Sea:\\ & \\ & a=18\\ & b=180\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{1{8}^{2}–180}\\ m& =\sqrt{324–180}\\ m& =\sqrt{144}\\ m& =12\\ & \\ \sqrt{18+6\sqrt{5}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{18+12}{2}}+\sqrt{\frac{18–12}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{15}+\sqrt{3}\end{array}$
24. $\begin{array}{cc}24–2\sqrt{143}& \\ & \\ \sqrt{24–2\sqrt{143}}& =\sqrt{24–\sqrt{572}}\\ & \\ & Sea:\\ & \\ & a=24\\ & b=572\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{2{4}^{2}–572}\\ m& =\sqrt{576–572}\\ m& =\sqrt{4}\\ m& =2\\ & \\ \sqrt{24–2\sqrt{143}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{24+2}{2}}–\sqrt{\frac{24–2}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{13}–\sqrt{11}\end{array}$
25. $\begin{array}{cc}30–20\sqrt{2}& \\ & \\ \sqrt{30–20\sqrt{2}}& =\sqrt{30–\sqrt{800}}\\ & \\ & Sea:\\ & \\ & a=30\\ & b=800\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{3{0}^{2}–800}\\ m& =\sqrt{900–800}\\ m& =\sqrt{100}\\ m& =10\\ & \\ \sqrt{30–20\sqrt{2}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{30+10}{2}}–\sqrt{\frac{30–10}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{20}–\sqrt{10}\\ & =\sqrt{5.{2}^{2}}–\sqrt{10}\\ & =2\sqrt{5}–\sqrt{10}\end{array}$
26. $\begin{array}{cc}9+6\sqrt{2}& \\ & \\ \sqrt{9+6\sqrt{2}}& =\sqrt{9+\sqrt{72}}\\ & \\ & Sea:\\ & \\ & a=9\\ & b=72\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{{9}^{2}–72}\\ m& =\sqrt{81–72}\\ m& =\sqrt{9}\\ m& =3\\ & \\ \sqrt{9+6\sqrt{2}}& =\sqrt{\frac{a+m}{2}}+\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{9+3}{2}}+\sqrt{\frac{9–3}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}+\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{6}+\sqrt{3}\end{array}$
27. $\begin{array}{cc}98–24\sqrt{5}& \\ & \\ \sqrt{98–24\sqrt{5}}& =\sqrt{98–\sqrt{2880}}\\ & \\ & Sea:\\ & \\ & a=98\\ & b=2880\\ & \\ m& =\sqrt{{a}^{2}–b}\\ m& =\sqrt{9{8}^{2}–2880}\\ m& =\sqrt{9604–2880}\\ m& =\sqrt{6724}\\ m& =82\\ & \\ \sqrt{98–24\sqrt{5}}& =\sqrt{\frac{a+m}{2}}–\sqrt{\frac{a–m}{2}}\\ & =\sqrt{\frac{98+82}{2}}–\sqrt{\frac{98–82}{2}}\\ & =\sqrt{\frac{}{\overline{)2}}}–\sqrt{\frac{}{\overline{)2}}}\\ & =\sqrt{90}–\sqrt{8}\\ & =\sqrt{10.{3}^{2}}–\sqrt{2.{2}^{2}}\\ & =3\sqrt{10}–2\sqrt{2}\end{array}$