Simplify Square Root of 70688

Here we will show you two methods that you can use to simplify the square root of 70688. In other words, we will show you how to find the square root of 70688 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.

√70688 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70688 to simplify the square root of 70688. 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 70688. The factors of 70688 are 1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, 1504, 2209, 4418, 8836, 17672, 35344, and 70688. Furthermore, the greatest perfect square on this list is 35344 and the square root of 35344 is 188. Therefore, A equals 188.

B = Calculate 70688 divided by the greatest perfect square from the list of all factors of 70688. We determined above that the greatest perfect square from the list of all factors of 70688 is 35344. Furthermore, 70688 divided by 35344 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 70688 in its simplest radical form as follows:

√70688 = A√B

√70688 = 188√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70688 to simplify the square root of 70688 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 70688 and then take the square root of that product. The prime factors that multiply together to make 70688 are 2 x 2 x 2 x 2 x 2 x 47 x 47. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 47 x 47 = 35344 and the square root of 35344 is 188. Therefore, A equals 188.

B = Divide 70688 by the number (A) squared. 188 squared is 35344 and 70688 divided by 35344 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 70688 in its simplest radical form as follows:

√70688 = A√B

√70688 = 188√2

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Simplify Square Root of 70689
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