Simplify Square Root of 15152

Here we will show you two methods that you can use to simplify the square root of 15152. In other words, we will show you how to find the square root of 15152 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.

√15152 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15152 to simplify the square root of 15152. 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 15152. The factors of 15152 are 1, 2, 4, 8, 16, 947, 1894, 3788, 7576, and 15152. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 15152 divided by the greatest perfect square from the list of all factors of 15152. We determined above that the greatest perfect square from the list of all factors of 15152 is 16. Furthermore, 15152 divided by 16 is 947, therefore B equals 947.

Now we have A and B and can get our answer to 15152 in its simplest radical form as follows:

√15152 = A√B

√15152 = 4√947

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15152 to simplify the square root of 15152 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 15152 and then take the square root of that product. The prime factors that multiply together to make 15152 are 2 x 2 x 2 x 2 x 947. 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 15152 by the number (A) squared. 4 squared is 16 and 15152 divided by 16 is 947. Therefore, B equals 947.

Once again we have A and B and can get our answer to 15152 in its simplest radical form as follows:

√15152 = A√B

√15152 = 4√947

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Simplify Square Root of 15153
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