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Q: How do you find the root of a monomial that is a perfect square?

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Say the monomial is 4a squared. To find the square root to must do each part seperately. So square root of 4 is 2 and the square root of a-squared is |a| because we do not know the sign of a. The answer is 2|a|. If there is anything that cannot be "square rooted" then it would stay under a square root sign and just multiply by 2a as well. The principal root of a number is only its positive root (you can understand that you are looking for the principal root from the sign in front of the radical, which is a positive one)

345 is not a perfect square and neither is its square root.

The idea is to take out perfect squares. The largest perfect square in this case is 256, which is the square of 16 (if you have trouble figuring this out, you can take out a smaller perfect square first, and then see if you find additional perfect squares). In any case, the end result should not have a factor that is a perfect square. Using the symbol "root()" for square root: root(512) = root(256 x 2) = root(256) x root(2) = 16 root(2)

Any integer is a perfect square oot (of its square). So 300 is a perfect square root of 90000.

Yes, a perfect square is a number that has an integer square root.

Related questions

Say the monomial is 4a squared. To find the square root to must do each part seperately. So square root of 4 is 2 and the square root of a-squared is |a| because we do not know the sign of a. The answer is 2|a|. If there is anything that cannot be "square rooted" then it would stay under a square root sign and just multiply by 2a as well. The principal root of a number is only its positive root (you can understand that you are looking for the principal root from the sign in front of the radical, which is a positive one)

If its square root can be expressed as a rational number then it is a perfect square. 9075 is not a perfect square. However, 9025 is.

5607 + 18 = 5625, a perfect square. The perfect square of a square root is the number you started with.

The sqrt. will be the length of one side.

345 is not a perfect square and neither is its square root.

200 is not a perfect square. Its square root is a fraction and the square root of a perfect square is always an integer.

30 is not a perfect square. Its square root is a fraction and the square root of a perfect square is always an integer.

500 is not a perfect square. Its square root is a fraction and the square root of a perfect square is always an integer.

38 is not a perfect square. Its square root is a fraction and the square root of a perfect square is always an integer.

A principal square root is any square root that's answer is positive, and a perfect square root is a square root that's answer is an integer.

The idea is to take out perfect squares. The largest perfect square in this case is 256, which is the square of 16 (if you have trouble figuring this out, you can take out a smaller perfect square first, and then see if you find additional perfect squares). In any case, the end result should not have a factor that is a perfect square. Using the symbol "root()" for square root: root(512) = root(256 x 2) = root(256) x root(2) = 16 root(2)

16 is a perfect square (of 4) and the square root of 256.

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