Simplify Square Root of 75645

Here we will show you two methods that you can use to simplify the square root of 75645. In other words, we will show you how to find the square root of 75645 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.

√75645 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75645 to simplify the square root of 75645. 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 75645. The factors of 75645 are 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, 1681, 1845, 5043, 8405, 15129, 25215, and 75645. Furthermore, the greatest perfect square on this list is 15129 and the square root of 15129 is 123. Therefore, A equals 123.

B = Calculate 75645 divided by the greatest perfect square from the list of all factors of 75645. We determined above that the greatest perfect square from the list of all factors of 75645 is 15129. Furthermore, 75645 divided by 15129 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 75645 in its simplest radical form as follows:

√75645 = A√B

√75645 = 123√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75645 to simplify the square root of 75645 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 75645 and then take the square root of that product. The prime factors that multiply together to make 75645 are 3 x 3 x 5 x 41 x 41. When we strip out the pairs only, we get 3 x 3 x 41 x 41 = 15129 and the square root of 15129 is 123. Therefore, A equals 123.

B = Divide 75645 by the number (A) squared. 123 squared is 15129 and 75645 divided by 15129 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 75645 in its simplest radical form as follows:

√75645 = A√B

√75645 = 123√5

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Simplify Square Root of 75646
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