Simplify Square Root of 48537

Here we will show you two methods that you can use to simplify the square root of 48537. In other words, we will show you how to find the square root of 48537 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.

√48537 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48537 to simplify the square root of 48537. 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 48537. The factors of 48537 are 1, 3, 9, 5393, 16179, and 48537. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 48537 divided by the greatest perfect square from the list of all factors of 48537. We determined above that the greatest perfect square from the list of all factors of 48537 is 9. Furthermore, 48537 divided by 9 is 5393, therefore B equals 5393.

Now we have A and B and can get our answer to 48537 in its simplest radical form as follows:

√48537 = A√B

√48537 = 3√5393

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48537 to simplify the square root of 48537 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 48537 and then take the square root of that product. The prime factors that multiply together to make 48537 are 3 x 3 x 5393. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 48537 by the number (A) squared. 3 squared is 9 and 48537 divided by 9 is 5393. Therefore, B equals 5393.

Once again we have A and B and can get our answer to 48537 in its simplest radical form as follows:

√48537 = A√B

√48537 = 3√5393

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Simplify Square Root of 48538
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