Question

Rationalisie the denominator of: 3/√5+√2​

Answer 1

`\longmapsto \: √(5) - √(2.)`

Explanation:

`\sf{(3)/(√(5) + √(2))}`

By rationalizing the denominator,

`=\sf{(3)/(√(5) + √(2)) * (√(5) - √(2))/(√(5) - √(2))}`

`=\sf{(3(√(5) - √(2)))/((√(5) + √(2))(√(5) - √(2)))}`

Applying the identity in the denominator:-

`\boxed{\underline{\red{\rm{(a + b)(a - b) = a^2 - b^2}}}}`

`=\sf{(3(√(5) - √(2)))/((√(5))^2 - (√(2))^2)}`

`=\sf{(3(√(5) - √(2)))/(5 - 2)}`

`=\sf{(3(√(5) - √(2)))/(3)}`

`=\sf{\frac{\\ot{3}(√(5) - √(2))}{\\ot{3}}}`

`\blue{\boxed{\underline{\rm{\therefore\:(3)/(√(5) + √(2)) = √(5) - √(2)}}}}`