Question

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

Answer 1

`\longmapsto √(7 ) + √(2) .`

Explanation:

`\sf{\:(5)/(√(7) - √(2))}`

By rationalizing the denominator,

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

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

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

`=\sf{(5(√(7) + √(2)))/(7 - 2)}`

`=\sf{(5(√(7) + √(2)))/(5)}`

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

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

Answer 2

`= √(7) + √(2)`

in alternate forms

`= 4.05996`

hope it helps