Simplify Square Root of 70624

Here we will show you two methods that you can use to simplify the square root of 70624. In other words, we will show you how to find the square root of 70624 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.

√70624 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70624 to simplify the square root of 70624. 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 70624. The factors of 70624 are 1, 2, 4, 8, 16, 32, 2207, 4414, 8828, 17656, 35312, and 70624. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 70624 divided by the greatest perfect square from the list of all factors of 70624. We determined above that the greatest perfect square from the list of all factors of 70624 is 16. Furthermore, 70624 divided by 16 is 4414, therefore B equals 4414.

Now we have A and B and can get our answer to 70624 in its simplest radical form as follows:

√70624 = A√B

√70624 = 4√4414

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70624 to simplify the square root of 70624 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 70624 and then take the square root of that product. The prime factors that multiply together to make 70624 are 2 x 2 x 2 x 2 x 2 x 2207. 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 70624 by the number (A) squared. 4 squared is 16 and 70624 divided by 16 is 4414. Therefore, B equals 4414.

Once again we have A and B and can get our answer to 70624 in its simplest radical form as follows:

√70624 = A√B

√70624 = 4√4414

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