Simplify Square Root of 77175

Here we will show you two methods that you can use to simplify the square root of 77175. In other words, we will show you how to find the square root of 77175 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.

√77175 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77175 to simplify the square root of 77175. 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 77175. The factors of 77175 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 49, 63, 75, 105, 147, 175, 225, 245, 315, 343, 441, 525, 735, 1029, 1225, 1575, 1715, 2205, 3087, 3675, 5145, 8575, 11025, 15435, 25725, and 77175. Furthermore, the greatest perfect square on this list is 11025 and the square root of 11025 is 105. Therefore, A equals 105.

B = Calculate 77175 divided by the greatest perfect square from the list of all factors of 77175. We determined above that the greatest perfect square from the list of all factors of 77175 is 11025. Furthermore, 77175 divided by 11025 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 77175 in its simplest radical form as follows:

√77175 = A√B

√77175 = 105√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77175 to simplify the square root of 77175 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 77175 and then take the square root of that product. The prime factors that multiply together to make 77175 are 3 x 3 x 5 x 5 x 7 x 7 x 7. When we strip out the pairs only, we get 3 x 3 x 5 x 5 x 7 x 7 = 11025 and the square root of 11025 is 105. Therefore, A equals 105.

B = Divide 77175 by the number (A) squared. 105 squared is 11025 and 77175 divided by 11025 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 77175 in its simplest radical form as follows:

√77175 = A√B

√77175 = 105√7

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