Simplify Square Root of 37532

Here we will show you two methods that you can use to simplify the square root of 37532. In other words, we will show you how to find the square root of 37532 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.

√37532 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37532 to simplify the square root of 37532. 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 37532. The factors of 37532 are 1, 2, 4, 11, 22, 44, 853, 1706, 3412, 9383, 18766, and 37532. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 37532 divided by the greatest perfect square from the list of all factors of 37532. We determined above that the greatest perfect square from the list of all factors of 37532 is 4. Furthermore, 37532 divided by 4 is 9383, therefore B equals 9383.

Now we have A and B and can get our answer to 37532 in its simplest radical form as follows:

√37532 = A√B

√37532 = 2√9383

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37532 to simplify the square root of 37532 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 37532 and then take the square root of that product. The prime factors that multiply together to make 37532 are 2 x 2 x 11 x 853. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 37532 by the number (A) squared. 2 squared is 4 and 37532 divided by 4 is 9383. Therefore, B equals 9383.

Once again we have A and B and can get our answer to 37532 in its simplest radical form as follows:

√37532 = A√B

√37532 = 2√9383

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Simplify Square Root of 37533
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