The monomial 36x⁸ is a perfect square. What is the square root of 36x⁸?

Recognize that the square root of 36 x n must be in the form 6 x n /2 , where n is even.
Analyze the given options to see which one matches the required form.
Determine that 6 x 4 is the only option that fits the form, implying n = 8 .
Conclude that the square root of 36 x n is 6 x 4 ​ .

Explanation

Understanding the problem We are given that 36 x n is a perfect square and asked to find its square root from the given options. Since 36 x n is a perfect square, n must be an even integer. The square root of 36 is 6. The square root of x n is x n /2 . Therefore, the square root of 36 x n is 6 x n /2 . We need to find which of the given options matches this form.

Analyzing the options Let's analyze the options:


Option 1: 6 x ′ - This is not a valid option because the exponent is not clearly defined.
Option 2: 6 x 4 - This matches the form 6 x n /2 . If n /2 = 4 , then n = 8 . Since 8 is an even integer, this is a valid option.
Option 3: 18 x 2 - This does not match the form 6 x n /2 because the coefficient is 18, not 6.
Option 4: 18 x 4 - This does not match the form 6 x n /2 because the coefficient is 18, not 6.

Determining the square root Therefore, the square root of 36 x n is 6 x 4 , which means n = 8 .

Final Answer The square root of 36 x n is 6 x 4 .


Examples
Understanding perfect squares and their square roots is fundamental in algebra and has practical applications. For instance, when calculating the area of a square, if you know the area is 36 x 8 , finding the side length involves taking the square root, which is 6 x 4 . This concept extends to various fields like engineering, where determining dimensions from area or volume often requires finding square roots or cube roots of algebraic expressions. It's also used in computer graphics for scaling and transformations.

Answered by GinnyAnswer | 2025-07-08

The square root of the monomial 36 x 8 is 6 x 4 , derived from the square root of 36 being 6 and the square root of x 8 being x 4 . Therefore, the final result is 6 x 4 .
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Answered by Anonymous | 2025-08-08