Simplify Square Root of 60572

Here we will show you two methods that you can use to simplify the square root of 60572. In other words, we will show you how to find the square root of 60572 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.

√60572 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60572 to simplify the square root of 60572. 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 60572. The factors of 60572 are 1, 2, 4, 19, 38, 76, 797, 1594, 3188, 15143, 30286, and 60572. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 60572 divided by the greatest perfect square from the list of all factors of 60572. We determined above that the greatest perfect square from the list of all factors of 60572 is 4. Furthermore, 60572 divided by 4 is 15143, therefore B equals 15143.

Now we have A and B and can get our answer to 60572 in its simplest radical form as follows:

√60572 = A√B

√60572 = 2√15143

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60572 to simplify the square root of 60572 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 60572 and then take the square root of that product. The prime factors that multiply together to make 60572 are 2 x 2 x 19 x 797. 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 60572 by the number (A) squared. 2 squared is 4 and 60572 divided by 4 is 15143. Therefore, B equals 15143.

Once again we have A and B and can get our answer to 60572 in its simplest radical form as follows:

√60572 = A√B

√60572 = 2√15143

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Simplify Square Root of 60573
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