Answered

IDNLearn.com offers a unique blend of expert answers and community-driven insights. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.

The monomial [tex]$36 x^4$[/tex] is a perfect square. What is the square root of [tex]$36 x^4$[/tex]?

A. [tex][tex]$6 x^2$[/tex][/tex]
B. [tex]$6 x^4$[/tex]
C. [tex]$18 x^2$[/tex]
D. [tex][tex]$18 x^4$[/tex][/tex]

Sagot :

GinnyAnsweridn
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].
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.