Simplify Square Root of 61700

Here we will show you two methods that you can use to simplify the square root of 61700. In other words, we will show you how to find the square root of 61700 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.

√61700 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 61700 to simplify the square root of 61700. 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 61700. The factors of 61700 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 617, 1234, 2468, 3085, 6170, 12340, 15425, 30850, and 61700. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 61700 divided by the greatest perfect square from the list of all factors of 61700. We determined above that the greatest perfect square from the list of all factors of 61700 is 100. Furthermore, 61700 divided by 100 is 617, therefore B equals 617.

Now we have A and B and can get our answer to 61700 in its simplest radical form as follows:

√61700 = A√B

√61700 = 10√617

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 61700 to simplify the square root of 61700 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 61700 and then take the square root of that product. The prime factors that multiply together to make 61700 are 2 x 2 x 5 x 5 x 617. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 61700 by the number (A) squared. 10 squared is 100 and 61700 divided by 100 is 617. Therefore, B equals 617.

Once again we have A and B and can get our answer to 61700 in its simplest radical form as follows:

√61700 = A√B

√61700 = 10√617

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Simplify Square Root of 61701
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