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].
