Simplify Square Root of 30752

Here we will show you two methods that you can use to simplify the square root of 30752. In other words, we will show you how to find the square root of 30752 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.

√30752 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30752 to simplify the square root of 30752. 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 30752. The factors of 30752 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 961, 992, 1922, 3844, 7688, 15376, and 30752. Furthermore, the greatest perfect square on this list is 15376 and the square root of 15376 is 124. Therefore, A equals 124.

B = Calculate 30752 divided by the greatest perfect square from the list of all factors of 30752. We determined above that the greatest perfect square from the list of all factors of 30752 is 15376. Furthermore, 30752 divided by 15376 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 30752 in its simplest radical form as follows:

√30752 = A√B

√30752 = 124√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30752 to simplify the square root of 30752 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 30752 and then take the square root of that product. The prime factors that multiply together to make 30752 are 2 x 2 x 2 x 2 x 2 x 31 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 31 x 31 = 15376 and the square root of 15376 is 124. Therefore, A equals 124.

B = Divide 30752 by the number (A) squared. 124 squared is 15376 and 30752 divided by 15376 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 30752 in its simplest radical form as follows:

√30752 = A√B

√30752 = 124√2

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Simplify Square Root of 30753
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