Question

Does anyone know how to rationalise the denominator ???

Answer 1

Multiply the entire expression by the radical denominator. This keeps the expression equal and makes the denominator 3, a whole number.

Explanation:

The denominator is irrational because it is a radical number, √3.

To rationalize the denominator, multiply the entire expression by √3. The denominator will become a whole number. This works because you multiply top and bottom by the same value.

`(3 + √(2) )/(√(3))`

`= ((√(3))(3 + √(2)) )/((√(3))(√(3)))`

`= ((√(3))(3 + √(2)) )/(3)`

√3 X √3 = 3 because:

√3 X √3 = √3²

Squaring a number and also finding its square root are opposites, or reverse operations. They cancel out

You probably need to simplify the rest of the equation too.

`((√(3))(3 + √(2)) )/(3)`

`= (3(√(3)) + (√(2))(√(3)))/(3)` Distribute over brackets

`= (3(√(3)) + √(2*3))/(3)` Simplify

`= (3(√(3)) + √(6))/(3)`

Some people use a more simplified version whether they simplify each term in the numerator:

`(3(√(3)) + √(6))/(3)` (3√3)÷3 = √3

`√(3) + (√(6))/(3)`