Question

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

Answer 1

`sqrt(32)sqrt(32)=(sqrt(32))^2=32`

Explanation:

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

Thus, by the definition of a square root, `sqrt(32)sqrt(32)=(sqrt(32))^2=32`

Answer 2

32

Explanation:

Another way of writing `sqrt32sqrt32` is

`32^(1/2)32^(1/2)`

which is the exponent form of that expression.

By the law of exponents, `x^ax^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 `1/2` for both of them, just add them together to find the exponent when you combine the bases together.

`1/2+ 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`.