# How do you simplify 3sqrt32-4sqrt63?

May 31, 2016

$12 \sqrt{2} - 12 \sqrt{7}$

#### Explanation:

To simplify a radical means to express it in the form $a \sqrt{b}$

where a is a rational number and $\sqrt{b} ,$ is a surd.

Rational numbers can be expressed in the form $\frac{a}{b}$ where a and b are integers.

example : $\frac{1}{2} , \frac{2}{3} , \frac{7}{8} \text{ and " 4" as 4} = \frac{4}{1}$

numbers which cannot be expressed in this form are called irrational. $\pi$ being an example of one.

A surd is a radical which cannot be reduced to a whole number.

$\sqrt{9} = 3 \text{ is not a surd but "sqrt3" is not a whole number and so is a surd.}$

now $\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2}$

and $\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3 \sqrt{7}$

$\Rightarrow 3 \sqrt{32} - 4 \sqrt{63} = 3 \times 4 \sqrt{2} - 4 \times 3 \sqrt{7}$

$= 12 \sqrt{2} - 12 \sqrt{7}$