Simplify Square Root of 53624

Here we will show you two methods that you can use to simplify the square root of 53624. In other words, we will show you how to find the square root of 53624 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.

√53624 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53624 to simplify the square root of 53624. 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 53624. The factors of 53624 are 1, 2, 4, 8, 6703, 13406, 26812, and 53624. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 53624 divided by the greatest perfect square from the list of all factors of 53624. We determined above that the greatest perfect square from the list of all factors of 53624 is 4. Furthermore, 53624 divided by 4 is 13406, therefore B equals 13406.

Now we have A and B and can get our answer to 53624 in its simplest radical form as follows:

√53624 = A√B

√53624 = 2√13406

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53624 to simplify the square root of 53624 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 53624 and then take the square root of that product. The prime factors that multiply together to make 53624 are 2 x 2 x 2 x 6703. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 53624 by the number (A) squared. 2 squared is 4 and 53624 divided by 4 is 13406. Therefore, B equals 13406.

Once again we have A and B and can get our answer to 53624 in its simplest radical form as follows:

√53624 = A√B

√53624 = 2√13406

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Simplify Square Root of 53625
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