Simplify Square Root of 700

Here we will show you two methods that you can use to simplify the square root of 700. In other words, we will show you how to find the square root of 700 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.

√700 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 700 to simplify the square root of 700. 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 700. The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 700 divided by the greatest perfect square from the list of all factors of 700. We determined above that the greatest perfect square from the list of all factors of 700 is 100. Furthermore, 700 divided by 100 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 700 in its simplest radical form as follows:

√700 = A√B

√700 = 10√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 700 to simplify the square root of 700 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 700 and then take the square root of that product. The prime factors that multiply together to make 700 are 2 x 2 x 5 x 5 x 7. 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 700 by the number (A) squared. 10 squared is 100 and 700 divided by 100 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 700 in its simplest radical form as follows:

√700 = A√B

√700 = 10√7

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Simplify Square Root of 701
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