Question

[Hà Annh]

Mọi người giúp mình vs ạ, mình đang cần gấp. Cảm ơn mn nhiều

\(\sqrt{49-5\sqrt{ }96}+\sqrt{49+5\sqrt{ }96}\)

\(\sqrt{13-\sqrt{ }160}+\sqrt{53+4\sqrt{ }90}\)

\(\sqrt{11-6\sqrt{ }2}+\sqrt{3-2\sqrt{ }2}\)

\(\sqrt{15-6\sqrt{ }6}+\sqrt{35-12\sqrt{ }6}\)

\(\sqrt{17-3\sqrt{ }32}+\sqrt{17+3\sqrt{ }32}\)

Answer 1

[Aki Tsuki]

\(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}=\sqrt{25-2\cdot5\cdot2\sqrt{6}+24}+\sqrt{25-2\cdot5\cdot2\sqrt{6}+24}=\sqrt{\left(5+2\sqrt{6}\right)^2}+\sqrt{\left(5-2\sqrt{6}\right)^2}=5+2\sqrt{6}+5-2\sqrt{6}=10\) ---

\(\sqrt{13-\sqrt{160}}+\sqrt{53+4\sqrt{90}}=\sqrt{8-2\sqrt{5}\cdot\sqrt{8}+5}+\sqrt{45+2\cdot3\sqrt{5}\cdot\sqrt{8}+8}=\sqrt{\left(\sqrt{8}-\sqrt{5}\right)^2}+\sqrt{\left(3\sqrt{5}+\sqrt{8}\right)^2}=\sqrt{8}-\sqrt{5}+3\sqrt{5}+\sqrt{8}=2\sqrt{8}+2\sqrt{5}\)

---

\(\sqrt{11-6\sqrt{2}}+\sqrt{3-2\sqrt{2}}=\sqrt{9-2\cdot3\cdot\sqrt{2}+2}+\sqrt{2-2\sqrt{2}+1}=\sqrt{\left(3-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{2}-1\right)^2}=3-\sqrt{2}+\sqrt{2}-1=2\)

---

\(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}=\sqrt{9-2\cdot3\cdot\sqrt{6}+6}+\sqrt{27-2\cdot\sqrt{27}\cdot\sqrt{8}+8}=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3\sqrt{3}-2\sqrt{2}\right)^2}=3-\sqrt{6}+3\sqrt{3}-2\sqrt{2}\)

---

\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}=\sqrt{9-2\cdot3\cdot2\sqrt{2}+8}+\sqrt{9+2\cdot2\cdot2\sqrt{2}+8}=\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(3+2\sqrt{2}\right)^2}=3-2\sqrt{2}+3+2\sqrt{2}=6\)

---

Answer 2

[T.Huyền]

\(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}\)

\(=\sqrt{25-2\times5\sqrt{24}+24}+\sqrt{25+2\times5\sqrt{24}+24}\)

\(=\sqrt{\left(5-\sqrt{24}\right)^2}+\sqrt{\left(5+\sqrt{24}\right)^2}\)

\(=5-\sqrt{24}+5+\sqrt{24}\)

\(=10\)