Simplify Square Root of 35574

Here we will show you two methods that you can use to simplify the square root of 35574. In other words, we will show you how to find the square root of 35574 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.

√35574 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 35574 to simplify the square root of 35574. 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 35574. The factors of 35574 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 49, 66, 77, 98, 121, 147, 154, 231, 242, 294, 363, 462, 539, 726, 847, 1078, 1617, 1694, 2541, 3234, 5082, 5929, 11858, 17787, and 35574. Furthermore, the greatest perfect square on this list is 5929 and the square root of 5929 is 77. Therefore, A equals 77.

B = Calculate 35574 divided by the greatest perfect square from the list of all factors of 35574. We determined above that the greatest perfect square from the list of all factors of 35574 is 5929. Furthermore, 35574 divided by 5929 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 35574 in its simplest radical form as follows:

√35574 = A√B

√35574 = 77√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 35574 to simplify the square root of 35574 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 35574 and then take the square root of that product. The prime factors that multiply together to make 35574 are 2 x 3 x 7 x 7 x 11 x 11. When we strip out the pairs only, we get 7 x 7 x 11 x 11 = 5929 and the square root of 5929 is 77. Therefore, A equals 77.

B = Divide 35574 by the number (A) squared. 77 squared is 5929 and 35574 divided by 5929 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 35574 in its simplest radical form as follows:

√35574 = A√B

√35574 = 77√6

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