Simplify Square Root of 95779

Here we will show you two methods that you can use to simplify the square root of 95779. In other words, we will show you how to find the square root of 95779 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.

√95779 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 95779 to simplify the square root of 95779. 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 95779. The factors of 95779 are 1, 19, 71, 1349, 5041, and 95779. Furthermore, the greatest perfect square on this list is 5041 and the square root of 5041 is 71. Therefore, A equals 71.

B = Calculate 95779 divided by the greatest perfect square from the list of all factors of 95779. We determined above that the greatest perfect square from the list of all factors of 95779 is 5041. Furthermore, 95779 divided by 5041 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 95779 in its simplest radical form as follows:

√95779 = A√B

√95779 = 71√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 95779 to simplify the square root of 95779 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 95779 and then take the square root of that product. The prime factors that multiply together to make 95779 are 19 x 71 x 71. When we strip out the pairs only, we get 71 x 71 = 5041 and the square root of 5041 is 71. Therefore, A equals 71.

B = Divide 95779 by the number (A) squared. 71 squared is 5041 and 95779 divided by 5041 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 95779 in its simplest radical form as follows:

√95779 = A√B

√95779 = 71√19

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Simplify Square Root of 95780
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