How do i simplify radical expressions step by step ?

Question

I need help trying to solve radical expressions. I'm stuck on what to do.

Answer 1

If you have a radical in the denominator of a fraction, you need to rationalise it so that the radical appears in the numerator only. For example, 1/√2 is changed to √2/2 by multiplying top and bottom by √2. This causes the radical in the denominator to disappear.

For more complicated fractions, use the difference of squares: for example:

(x+3)/(x+√5). Multiply top and bottom by x-√5:

(x+3)(x-√5)/(x²-5)=(x²+3x-x√5-3√5)/(x²-5).

This deals with square roots, but for other roots, such as cube roots the process may be more complicated to rationalise the radical.