Question

Rationalisie the denominator of: 2/√7+√5​

Answer 1

`\longmapsto √(7) - √(5) .`

Explanation:

`\sf{\:(2)/(√(7) + √(5))}`

By rationalizing the denominator,

`=\sf{(2)/(√(7) + √(5))* (√(7) - √(5))/(√(7) - √(5))}`

`=\sf{(2(√(7) - √(5)))/((√(7) + √(5))(√(7) - √(5)))}`

`=\sf{(2(√(7) - √(5)))/((√(7))^2 - (√(5))^2)}`

`=\sf{(2(√(7) - √(5)))/(7 - 5)}`

`=\sf{(2(√(7) - √(5)))/(2)}`

`=\sf{\frac{\\ot{2}(√(7) - √(5))}{\\ot{2}}}`

`\boxed{\underline{\rm{\therefore\:(2)/(√(7) + √(5)) = √(7) - √(5)}}}`