Simplify Square Root of 79210

Here we will show you two methods that you can use to simplify the square root of 79210. In other words, we will show you how to find the square root of 79210 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.

√79210 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 79210 to simplify the square root of 79210. 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 79210. The factors of 79210 are 1, 2, 5, 10, 89, 178, 445, 890, 7921, 15842, 39605, and 79210. Furthermore, the greatest perfect square on this list is 7921 and the square root of 7921 is 89. Therefore, A equals 89.

B = Calculate 79210 divided by the greatest perfect square from the list of all factors of 79210. We determined above that the greatest perfect square from the list of all factors of 79210 is 7921. Furthermore, 79210 divided by 7921 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 79210 in its simplest radical form as follows:

√79210 = A√B

√79210 = 89√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 79210 to simplify the square root of 79210 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 79210 and then take the square root of that product. The prime factors that multiply together to make 79210 are 2 x 5 x 89 x 89. When we strip out the pairs only, we get 89 x 89 = 7921 and the square root of 7921 is 89. Therefore, A equals 89.

B = Divide 79210 by the number (A) squared. 89 squared is 7921 and 79210 divided by 7921 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 79210 in its simplest radical form as follows:

√79210 = A√B

√79210 = 89√10

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Simplify Square Root of 79211
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