To determine the square root of the monomial [tex]\(36 x^4\)[/tex], we need to take the square root of both the numerical coefficient and the variable part.
Let's break it down step by step:
1. Square root of the numerical coefficient:
- The numerical coefficient in the monomial is [tex]\(36\)[/tex].
- The square root of [tex]\(36\)[/tex] is [tex]\(6\)[/tex] because [tex]\(6^2 = 36\)[/tex].
2. Square root of the variable term:
- The variable term in the monomial is [tex]\(x^4\)[/tex].
- The square root of [tex]\(x^4\)[/tex] is [tex]\(x^2\)[/tex] because [tex]\((x^2)^2 = x^4\)[/tex].
3. Combine the results:
- The square root of [tex]\(36\)[/tex] is [tex]\(6\)[/tex].
- The square root of [tex]\(x^4\)[/tex] is [tex]\(x^2\)[/tex].
- Therefore, the square root of [tex]\(36 x^4\)[/tex] is [tex]\(6 x^2\)[/tex].
So, the correct answer is [tex]\(6 x^2\)[/tex].
