What is the square root of [tex][tex]$16 x^{36}$[/tex][/tex]?

A. [tex][tex]$4 x^6$[/tex][/tex]
B. [tex][tex]$4 x^{18}$[/tex][/tex]
C. [tex][tex]$8 x^6$[/tex][/tex]
D. [tex][tex]$8 x^{18}$[/tex][/tex]



Answer :

To find the square root of [tex]\(16 x^{36}\)[/tex], we need to consider both the coefficient and the exponent separately.

First, let's consider the coefficient 16. The square root of 16 is obtained by finding a number which, when multiplied by itself, gives 16. We have:

[tex]\[ \sqrt{16} = 4 \][/tex]

Next, let's consider the variable term [tex]\(x^{36}\)[/tex]. The square root of [tex]\(x^{36}\)[/tex] is obtained by dividing the exponent by 2, because taking the square root of a power involves halving the exponent:

[tex]\[ \sqrt{x^{36}} = x^{36/2} = x^{18} \][/tex]

Now, combining the two results, we get:

[tex]\[ \sqrt{16 x^{36}} = 4 \cdot x^{18} = 4 x^{18} \][/tex]

Therefore, the square root of [tex]\(16 x^{36}\)[/tex] is [tex]\(\boxed{4 x^{18}}\)[/tex].