Simplify Square Root of 10952

Here we will show you two methods that you can use to simplify the square root of 10952. In other words, we will show you how to find the square root of 10952 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.

√10952 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10952 to simplify the square root of 10952. 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 10952. The factors of 10952 are 1, 2, 4, 8, 37, 74, 148, 296, 1369, 2738, 5476, and 10952. Furthermore, the greatest perfect square on this list is 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Calculate 10952 divided by the greatest perfect square from the list of all factors of 10952. We determined above that the greatest perfect square from the list of all factors of 10952 is 5476. Furthermore, 10952 divided by 5476 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 10952 in its simplest radical form as follows:

√10952 = A√B

√10952 = 74√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10952 to simplify the square root of 10952 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 10952 and then take the square root of that product. The prime factors that multiply together to make 10952 are 2 x 2 x 2 x 37 x 37. When we strip out the pairs only, we get 2 x 2 x 37 x 37 = 5476 and the square root of 5476 is 74. Therefore, A equals 74.

B = Divide 10952 by the number (A) squared. 74 squared is 5476 and 10952 divided by 5476 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 10952 in its simplest radical form as follows:

√10952 = A√B

√10952 = 74√2

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Simplify Square Root of 10953
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