Simplify Square Root of 84270

Here we will show you two methods that you can use to simplify the square root of 84270. In other words, we will show you how to find the square root of 84270 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√84270 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84270 to simplify the square root of 84270. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 84270. The factors of 84270 are 1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590, 2809, 5618, 8427, 14045, 16854, 28090, 42135, and 84270. Furthermore, the greatest perfect square on this list is 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Calculate 84270 divided by the greatest perfect square from the list of all factors of 84270. We determined above that the greatest perfect square from the list of all factors of 84270 is 2809. Furthermore, 84270 divided by 2809 is 30, therefore B equals 30.

Now we have A and B and can get our answer to 84270 in its simplest radical form as follows:

√84270 = A√B

√84270 = 53√30

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84270 to simplify the square root of 84270 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 84270 and then take the square root of that product. The prime factors that multiply together to make 84270 are 2 x 3 x 5 x 53 x 53. When we strip out the pairs only, we get 53 x 53 = 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Divide 84270 by the number (A) squared. 53 squared is 2809 and 84270 divided by 2809 is 30. Therefore, B equals 30.

Once again we have A and B and can get our answer to 84270 in its simplest radical form as follows:

√84270 = A√B

√84270 = 53√30

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Simplify Square Root of 84271
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