# How do you simplify radical expressions with variables?

Jan 6, 2015

This is easy! If you want to multiply this are the rules: First coefficients are multiplied with each other and the sub-radical amounts each other, placing the latter product under the radical sign common and the result is simplified.

Let's go: $2 \sqrt{5}$ times $3 \sqrt{10}$

2sqrt5 × 3sqrt10 = 2 × 3sqrt(5×10)=6sqrt50

= 6sqrt(2·5^2)

$= 30 \sqrt{2}$

Now if you want to divide, then the coefficients are divided among themselves and sub-radical amounts each other, placing the latter quotient under the radical common and the result is simplified.

$2 \sqrt[3]{81 {x}^{7}}$ by $3 \sqrt[3]{3 {x}^{2}}$

$\frac{2 \sqrt[3]{81 {x}^{7}}}{3 \sqrt[3]{3 {x}^{2}}} = \frac{2}{3} \sqrt[3]{\frac{81 {x}^{7}}{3 {x}^{2}}} = \frac{2}{3} \sqrt[3]{27 {x}^{5}}$

2/3 root3 (3^3·x^3·x^2) = 2xroot3 (x^2)