Simplify Square Root of 60464

Here we will show you two methods that you can use to simplify the square root of 60464. In other words, we will show you how to find the square root of 60464 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.

√60464 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60464 to simplify the square root of 60464. 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 60464. The factors of 60464 are 1, 2, 4, 8, 16, 3779, 7558, 15116, 30232, and 60464. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 60464 divided by the greatest perfect square from the list of all factors of 60464. We determined above that the greatest perfect square from the list of all factors of 60464 is 16. Furthermore, 60464 divided by 16 is 3779, therefore B equals 3779.

Now we have A and B and can get our answer to 60464 in its simplest radical form as follows:

√60464 = A√B

√60464 = 4√3779

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60464 to simplify the square root of 60464 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 60464 and then take the square root of that product. The prime factors that multiply together to make 60464 are 2 x 2 x 2 x 2 x 3779. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 60464 by the number (A) squared. 4 squared is 16 and 60464 divided by 16 is 3779. Therefore, B equals 3779.

Once again we have A and B and can get our answer to 60464 in its simplest radical form as follows:

√60464 = A√B

√60464 = 4√3779

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Simplify Square Root of 60465
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