Simplify Square Root of 97470

Here we will show you two methods that you can use to simplify the square root of 97470. In other words, we will show you how to find the square root of 97470 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.

√97470 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97470 to simplify the square root of 97470. 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 97470. The factors of 97470 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 27, 30, 38, 45, 54, 57, 90, 95, 114, 135, 171, 190, 270, 285, 342, 361, 513, 570, 722, 855, 1026, 1083, 1710, 1805, 2166, 2565, 3249, 3610, 5130, 5415, 6498, 9747, 10830, 16245, 19494, 32490, 48735, and 97470. Furthermore, the greatest perfect square on this list is 3249 and the square root of 3249 is 57. Therefore, A equals 57.

B = Calculate 97470 divided by the greatest perfect square from the list of all factors of 97470. We determined above that the greatest perfect square from the list of all factors of 97470 is 3249. Furthermore, 97470 divided by 3249 is 30, therefore B equals 30.

Now we have A and B and can get our answer to 97470 in its simplest radical form as follows:

√97470 = A√B

√97470 = 57√30

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97470 to simplify the square root of 97470 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 97470 and then take the square root of that product. The prime factors that multiply together to make 97470 are 2 x 3 x 3 x 3 x 5 x 19 x 19. When we strip out the pairs only, we get 3 x 3 x 19 x 19 = 3249 and the square root of 3249 is 57. Therefore, A equals 57.

B = Divide 97470 by the number (A) squared. 57 squared is 3249 and 97470 divided by 3249 is 30. Therefore, B equals 30.

Once again we have A and B and can get our answer to 97470 in its simplest radical form as follows:

√97470 = A√B

√97470 = 57√30

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 97471
Here is the next square root on our list that we have simplifed for you.