Question

\(\dfrac{1}{3}\sqrt{45}-\sqrt{20}+\sqrt{9+4\sqrt{5}}\)

Answer 1

\(\dfrac{1}{3}\sqrt{45}-\sqrt{20}+\sqrt{9+4\sqrt{5}}\)

= \(\dfrac{1}{3}.3.\sqrt{5}-2\sqrt{5}+\sqrt{\left(2+\sqrt{5}\right)^2}\)

= \(\sqrt{5}-2\sqrt{5}+2+\sqrt{5}=2\)

Answer 2

\(\dfrac{1}{3}\sqrt{45}-\sqrt{20}+\sqrt{9+4\sqrt{5}}=\dfrac{1}{3}\sqrt{9.5}-\sqrt{4.5}+\sqrt{2^2+2.2.\sqrt{5}+\left(\sqrt{5}\right)^2}\)

\(\dfrac{1}{3}.3\sqrt{5}-2\sqrt{5}+\sqrt{\left(2+\sqrt{5}\right)^2}=\sqrt{5}-2\sqrt{5}+\left|2+\sqrt{5}\right|\)

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

Answer 3

`1/3sqrt{45}-sqrt{20}+sqrt{9+4sqrt5}`

`=1/3*3sqrt5-2sqrt5+sqrt{(sqrt5+2)^2}`

`=sqrt5-2sqrt5+sqrt5+2=2`