Simplify Square Root of 65970

Here we will show you two methods that you can use to simplify the square root of 65970. In other words, we will show you how to find the square root of 65970 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.

√65970 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 65970 to simplify the square root of 65970. 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 65970. The factors of 65970 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 733, 1466, 2199, 3665, 4398, 6597, 7330, 10995, 13194, 21990, 32985, and 65970. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 65970 divided by the greatest perfect square from the list of all factors of 65970. We determined above that the greatest perfect square from the list of all factors of 65970 is 9. Furthermore, 65970 divided by 9 is 7330, therefore B equals 7330.

Now we have A and B and can get our answer to 65970 in its simplest radical form as follows:

√65970 = A√B

√65970 = 3√7330

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 65970 to simplify the square root of 65970 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 65970 and then take the square root of that product. The prime factors that multiply together to make 65970 are 2 x 3 x 3 x 5 x 733. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 65970 by the number (A) squared. 3 squared is 9 and 65970 divided by 9 is 7330. Therefore, B equals 7330.

Once again we have A and B and can get our answer to 65970 in its simplest radical form as follows:

√65970 = A√B

√65970 = 3√7330

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Simplify Square Root of 65971
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