# Math Help - radical simplification

1. ## radical simplification

hello can someone please show how to simplify this
20√3-40
---
√2

to 20(√3-√2)

thanks in advance

2. Originally Posted by jepal
hello can someone please show how to simplify this
20√3-40
---
√2

to 20(√3-√2)

thanks in advance
$20\sqrt{3} - \dfrac{40}{\sqrt{2}}$

Multiply the numerator and denominator of the second quotient by the irrational denominator to get rid of the square root:

$20\sqrt{3} - \dfrac{40}{\sqrt{2}} = 20\sqrt{3} - \dfrac{40 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = 20\sqrt{3} - \dfrac{40 \cdot \sqrt{2}}{2} = 20\sqrt{3} - 20 \cdot \sqrt{2}$

Factor out 20 and you'll get the given result.

3. thank u!!