Simplify Square Root of 67995

Here we will show you two methods that you can use to simplify the square root of 67995. In other words, we will show you how to find the square root of 67995 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.

√67995 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 67995 to simplify the square root of 67995. 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 67995. The factors of 67995 are 1, 3, 5, 9, 15, 45, 1511, 4533, 7555, 13599, 22665, and 67995. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 67995 divided by the greatest perfect square from the list of all factors of 67995. We determined above that the greatest perfect square from the list of all factors of 67995 is 9. Furthermore, 67995 divided by 9 is 7555, therefore B equals 7555.

Now we have A and B and can get our answer to 67995 in its simplest radical form as follows:

√67995 = A√B

√67995 = 3√7555

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 67995 to simplify the square root of 67995 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 67995 and then take the square root of that product. The prime factors that multiply together to make 67995 are 3 x 3 x 5 x 1511. 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 67995 by the number (A) squared. 3 squared is 9 and 67995 divided by 9 is 7555. Therefore, B equals 7555.

Once again we have A and B and can get our answer to 67995 in its simplest radical form as follows:

√67995 = A√B

√67995 = 3√7555

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Simplify Square Root of 67996
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