Question

\(\sqrt{20}-\sqrt{21-4\sqrt{5}}\)

Answer 1

`sqrt(20)-sqrt(21-4sqrt5)=2\sqrt5-sqrt((2\sqrt5)^2-2.2sqrt5 .1+1^2)=2\sqrt5-sqrt((2sqrt5-1)^2)=2sqrt5-2sqrt5+1=1`

Answer 2

`@` `\text {Ans}`

`\downarrow`

`\sqrt {20} -` \(\sqrt {21 - 4 \sqrt {5}}\)

`= 2 \sqrt {5} - \sqrt {20 + 1 - 4 \sqrt {5}}`

`= 2 \sqrt {5} - \sqrt {(2\sqrt {5})^2 - 2*2 \sqrt {5} + 1}`

`= 2 \sqrt {5} - \sqrt {(2 \sqrt {5} - 1)^2}`

`= 2 \sqrt {5} - 2 \sqrt {5} + 1`

`= 1`