Simplify Square Root of 77315

Here we will show you two methods that you can use to simplify the square root of 77315. In other words, we will show you how to find the square root of 77315 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.

√77315 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77315 to simplify the square root of 77315. 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 77315. The factors of 77315 are 1, 5, 7, 35, 47, 235, 329, 1645, 2209, 11045, 15463, and 77315. Furthermore, the greatest perfect square on this list is 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Calculate 77315 divided by the greatest perfect square from the list of all factors of 77315. We determined above that the greatest perfect square from the list of all factors of 77315 is 2209. Furthermore, 77315 divided by 2209 is 35, therefore B equals 35.

Now we have A and B and can get our answer to 77315 in its simplest radical form as follows:

√77315 = A√B

√77315 = 47√35

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77315 to simplify the square root of 77315 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 77315 and then take the square root of that product. The prime factors that multiply together to make 77315 are 5 x 7 x 47 x 47. When we strip out the pairs only, we get 47 x 47 = 2209 and the square root of 2209 is 47. Therefore, A equals 47.

B = Divide 77315 by the number (A) squared. 47 squared is 2209 and 77315 divided by 2209 is 35. Therefore, B equals 35.

Once again we have A and B and can get our answer to 77315 in its simplest radical form as follows:

√77315 = A√B

√77315 = 47√35

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Simplify Square Root of 77316
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