# How do you simplify sqrt(32)sqrt(32)?

Feb 13, 2016

$\sqrt{32} \sqrt{32} = {\left(\sqrt{32}\right)}^{2} = 32$

#### Explanation:

By definition, the square root of a number is the value which, when multiplied by itself, produces that number. That is, ${\left(\sqrt{x}\right)}^{2} = x$ for all $x$.

Thus, by the definition of a square root, $\sqrt{32} \sqrt{32} = {\left(\sqrt{32}\right)}^{2} = 32$

Feb 13, 2016

32

#### Explanation:

Another way of writing $\sqrt{32} \sqrt{32}$ is

${32}^{\frac{1}{2}} {32}^{\frac{1}{2}}$

which is the exponent form of that expression.

By the law of exponents, ${x}^{a} {x}^{b} = {x}^{a + b}$ where x is the base.

(Remember, the bases has to be the same number for this formula to work.)

Since the exponents of 32 in this problem is $\frac{1}{2}$ for both of them, just add them together to find the exponent when you combine the bases together.

$\frac{1}{2} + \frac{1}{2} = 1$.

So the simplified form is ${32}^{1}$ and any base with an exponent of one is equal to the base itself.

${32}^{1} = 32$.