Simplify Square Root of 71415

Here we will show you two methods that you can use to simplify the square root of 71415. In other words, we will show you how to find the square root of 71415 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.

√71415 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 71415 to simplify the square root of 71415. 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 71415. The factors of 71415 are 1, 3, 5, 9, 15, 23, 27, 45, 69, 115, 135, 207, 345, 529, 621, 1035, 1587, 2645, 3105, 4761, 7935, 14283, 23805, and 71415. Furthermore, the greatest perfect square on this list is 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Calculate 71415 divided by the greatest perfect square from the list of all factors of 71415. We determined above that the greatest perfect square from the list of all factors of 71415 is 4761. Furthermore, 71415 divided by 4761 is 15, therefore B equals 15.

Now we have A and B and can get our answer to 71415 in its simplest radical form as follows:

√71415 = A√B

√71415 = 69√15

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 71415 to simplify the square root of 71415 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 71415 and then take the square root of that product. The prime factors that multiply together to make 71415 are 3 x 3 x 3 x 5 x 23 x 23. When we strip out the pairs only, we get 3 x 3 x 23 x 23 = 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Divide 71415 by the number (A) squared. 69 squared is 4761 and 71415 divided by 4761 is 15. Therefore, B equals 15.

Once again we have A and B and can get our answer to 71415 in its simplest radical form as follows:

√71415 = A√B

√71415 = 69√15

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