Simplify Square Root of 70070

Here we will show you two methods that you can use to simplify the square root of 70070. In other words, we will show you how to find the square root of 70070 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.

√70070 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70070 to simplify the square root of 70070. 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 70070. The factors of 70070 are 1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 49, 55, 65, 70, 77, 91, 98, 110, 130, 143, 154, 182, 245, 286, 385, 455, 490, 539, 637, 715, 770, 910, 1001, 1078, 1274, 1430, 2002, 2695, 3185, 5005, 5390, 6370, 7007, 10010, 14014, 35035, and 70070. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 70070 divided by the greatest perfect square from the list of all factors of 70070. We determined above that the greatest perfect square from the list of all factors of 70070 is 49. Furthermore, 70070 divided by 49 is 1430, therefore B equals 1430.

Now we have A and B and can get our answer to 70070 in its simplest radical form as follows:

√70070 = A√B

√70070 = 7√1430

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70070 to simplify the square root of 70070 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 70070 and then take the square root of that product. The prime factors that multiply together to make 70070 are 2 x 5 x 7 x 7 x 11 x 13. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 70070 by the number (A) squared. 7 squared is 49 and 70070 divided by 49 is 1430. Therefore, B equals 1430.

Once again we have A and B and can get our answer to 70070 in its simplest radical form as follows:

√70070 = A√B

√70070 = 7√1430

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