Simplify Square Root of 53240

Here we will show you two methods that you can use to simplify the square root of 53240. In other words, we will show you how to find the square root of 53240 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.

√53240 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53240 to simplify the square root of 53240. 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 53240. The factors of 53240 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 121, 220, 242, 440, 484, 605, 968, 1210, 1331, 2420, 2662, 4840, 5324, 6655, 10648, 13310, 26620, and 53240. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 53240 divided by the greatest perfect square from the list of all factors of 53240. We determined above that the greatest perfect square from the list of all factors of 53240 is 484. Furthermore, 53240 divided by 484 is 110, therefore B equals 110.

Now we have A and B and can get our answer to 53240 in its simplest radical form as follows:

√53240 = A√B

√53240 = 22√110

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53240 to simplify the square root of 53240 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 53240 and then take the square root of that product. The prime factors that multiply together to make 53240 are 2 x 2 x 2 x 5 x 11 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 53240 by the number (A) squared. 22 squared is 484 and 53240 divided by 484 is 110. Therefore, B equals 110.

Once again we have A and B and can get our answer to 53240 in its simplest radical form as follows:

√53240 = A√B

√53240 = 22√110

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Simplify Square Root of 53241
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