Simplify Square Root of 75537

Here we will show you two methods that you can use to simplify the square root of 75537. In other words, we will show you how to find the square root of 75537 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.

√75537 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75537 to simplify the square root of 75537. 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 75537. The factors of 75537 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 109, 231, 327, 693, 763, 981, 1199, 2289, 3597, 6867, 8393, 10791, 25179, and 75537. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 75537 divided by the greatest perfect square from the list of all factors of 75537. We determined above that the greatest perfect square from the list of all factors of 75537 is 9. Furthermore, 75537 divided by 9 is 8393, therefore B equals 8393.

Now we have A and B and can get our answer to 75537 in its simplest radical form as follows:

√75537 = A√B

√75537 = 3√8393

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75537 to simplify the square root of 75537 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 75537 and then take the square root of that product. The prime factors that multiply together to make 75537 are 3 x 3 x 7 x 11 x 109. 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 75537 by the number (A) squared. 3 squared is 9 and 75537 divided by 9 is 8393. Therefore, B equals 8393.

Once again we have A and B and can get our answer to 75537 in its simplest radical form as follows:

√75537 = A√B

√75537 = 3√8393

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Simplify Square Root of 75538
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