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

2 Answers
Feb 13, 2016

Answer:

#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#

Feb 13, 2016

Answer:

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#.