Question

Rationalize the denominators

Answer 1

`(2√(3)+5√(2))/(3√(3)-2√(2)  )` is equal to
`2+√(6)`

Explanation:

Consider the given fraction,

`(2√(3)+5√(2))/(3√(3)-2√(2)  )`

We are required to rational denominator,

Multiply and divide numerator by
`\Rightarrow (2√(3)+5√(2))/(3√(3)-2√(2)) * (3√(3)+2√(2))/(3√(3)+2√(2))` , we get,

Using identity ,
`(a-b)(a+b)=a^2-b^2` in denominator, we get,

`\Rightarrow (2√(3)+5√(2))/(3√(3)-2√(2)) * (3√(3)+2√(2))/(3√(3)+2√(2))=((2√(3)+5√(2))(3√(3)+2√(2)))/((3√(3))^2-(2√(2))^2))`

`\Rightarrow ((2√(3)+5√(2))(3√(3)+2√(2)))/((3√(3))^2-(2√(2))^2))=((2√(3)+5√(2))(3√(3)+2√(2)))/(27-8)\\\\\\\\`

On solving further , we get,

`\Rightarrow ((2√(3)+5√(2))(3√(3)+2√(2)))/((3√(3))^2-(2√(2))^2))=(38+19√(6))/(19)`

solving , we get,

`\Rightarrow (38+19√(6))/(19)=2+√(6)`

Thus,
`(2√(3)+5√(2))/(3√(3)-2√(2)  )` is equal to
`2+√(6)`