Simplify Square Root of 6132

Here we will show you two methods that you can use to simplify the square root of 6132. In other words, we will show you how to find the square root of 6132 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.

√6132 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 6132 to simplify the square root of 6132. 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 6132. The factors of 6132 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 73, 84, 146, 219, 292, 438, 511, 876, 1022, 1533, 2044, 3066, and 6132. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 6132 divided by the greatest perfect square from the list of all factors of 6132. We determined above that the greatest perfect square from the list of all factors of 6132 is 4. Furthermore, 6132 divided by 4 is 1533, therefore B equals 1533.

Now we have A and B and can get our answer to 6132 in its simplest radical form as follows:

√6132 = A√B

√6132 = 2√1533

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 6132 to simplify the square root of 6132 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 6132 and then take the square root of that product. The prime factors that multiply together to make 6132 are 2 x 2 x 3 x 7 x 73. 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 6132 by the number (A) squared. 2 squared is 4 and 6132 divided by 4 is 1533. Therefore, B equals 1533.

Once again we have A and B and can get our answer to 6132 in its simplest radical form as follows:

√6132 = A√B

√6132 = 2√1533

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Simplify Square Root of 6133
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