Simplify Square Root of 8470

Here we will show you two methods that you can use to simplify the square root of 8470. In other words, we will show you how to find the square root of 8470 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.

√8470 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 8470 to simplify the square root of 8470. 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 8470. The factors of 8470 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 121, 154, 242, 385, 605, 770, 847, 1210, 1694, 4235, and 8470. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 8470 divided by the greatest perfect square from the list of all factors of 8470. We determined above that the greatest perfect square from the list of all factors of 8470 is 121. Furthermore, 8470 divided by 121 is 70, therefore B equals 70.

Now we have A and B and can get our answer to 8470 in its simplest radical form as follows:

√8470 = A√B

√8470 = 11√70

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 8470 to simplify the square root of 8470 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 8470 and then take the square root of that product. The prime factors that multiply together to make 8470 are 2 x 5 x 7 x 11 x 11. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 8470 by the number (A) squared. 11 squared is 121 and 8470 divided by 121 is 70. Therefore, B equals 70.

Once again we have A and B and can get our answer to 8470 in its simplest radical form as follows:

√8470 = A√B

√8470 = 11√70

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