Simplify Square Root of 15136

Here we will show you two methods that you can use to simplify the square root of 15136. In other words, we will show you how to find the square root of 15136 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.

√15136 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15136 to simplify the square root of 15136. 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 15136. The factors of 15136 are 1, 2, 4, 8, 11, 16, 22, 32, 43, 44, 86, 88, 172, 176, 344, 352, 473, 688, 946, 1376, 1892, 3784, 7568, and 15136. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 15136 divided by the greatest perfect square from the list of all factors of 15136. We determined above that the greatest perfect square from the list of all factors of 15136 is 16. Furthermore, 15136 divided by 16 is 946, therefore B equals 946.

Now we have A and B and can get our answer to 15136 in its simplest radical form as follows:

√15136 = A√B

√15136 = 4√946

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15136 to simplify the square root of 15136 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 15136 and then take the square root of that product. The prime factors that multiply together to make 15136 are 2 x 2 x 2 x 2 x 2 x 11 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 15136 by the number (A) squared. 4 squared is 16 and 15136 divided by 16 is 946. Therefore, B equals 946.

Once again we have A and B and can get our answer to 15136 in its simplest radical form as follows:

√15136 = A√B

√15136 = 4√946

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Simplify Square Root of 15137
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