Simplify Square Root of 62658

Here we will show you two methods that you can use to simplify the square root of 62658. In other words, we will show you how to find the square root of 62658 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.

√62658 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 62658 to simplify the square root of 62658. 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 62658. The factors of 62658 are 1, 2, 3, 6, 9, 18, 59, 118, 177, 354, 531, 1062, 3481, 6962, 10443, 20886, 31329, and 62658. Furthermore, the greatest perfect square on this list is 31329 and the square root of 31329 is 177. Therefore, A equals 177.

B = Calculate 62658 divided by the greatest perfect square from the list of all factors of 62658. We determined above that the greatest perfect square from the list of all factors of 62658 is 31329. Furthermore, 62658 divided by 31329 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 62658 in its simplest radical form as follows:

√62658 = A√B

√62658 = 177√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 62658 to simplify the square root of 62658 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 62658 and then take the square root of that product. The prime factors that multiply together to make 62658 are 2 x 3 x 3 x 59 x 59. When we strip out the pairs only, we get 3 x 3 x 59 x 59 = 31329 and the square root of 31329 is 177. Therefore, A equals 177.

B = Divide 62658 by the number (A) squared. 177 squared is 31329 and 62658 divided by 31329 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 62658 in its simplest radical form as follows:

√62658 = A√B

√62658 = 177√2

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Simplify Square Root of 62659
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