Question

\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)

Answer 1

\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)

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

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

\(=2\sqrt{5}+2+\sqrt{5}-2\)

\(=3\sqrt{5}\)

Answer 2

tham khảo

= √( 2√5 + 2)² + √(√5  2)²

⁼ | 2√5 + 2| + | √5 -2

= 2√5 + 2 + √5 - 2

= 3√5