Question

Please help!
what is the simplest form of the expression sqrt 2-sqrt 10/sqrt 2+sqrt 10

Answer 1

`(1)/(2)(√(5)-3)`

Explanation:

Given expression,

`(√(2)-√(10))/(√(2)+√(10))`

By rationalising the denominator,

`=(√(2)-√(10))/(√(2)+√(10))*(√(2)-√(10))/(√(2)-√(10))`

`=((√(2)-√(10))^2)/((√(2))^2-(√(10))^2)`

( ∵ ( a + b ) ( a - b ) = a² - b² )

`=((√(2)-√(10))^2)/(2-10)`

`=(2+10-2√(20))/(-8)`

( ∵ (a + b)² = a² + 2ab + b² )

`=-(1)/(8)(12-4√(5))`

`=-(1)/(2)(3-√(5))`

`=(1)/(2)(√(5)-3)`

Answer 2

`√(2)-√(5)+√(10)`

Explanation:

we have

`√(2)-(√(10))/(√(2)) +√(10)`

we know that

`√(10)=√(2)*√(5)`

substitute

`√(2)-(√(2)*√(5))/(√(2)) +√(10)`

simplify

`√(2)-√(5)+√(10)`