Simplify Square Root of 97853

Here we will show you two methods that you can use to simplify the square root of 97853. In other words, we will show you how to find the square root of 97853 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.

√97853 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97853 to simplify the square root of 97853. 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 97853. The factors of 97853 are 1, 7, 49, 1997, 13979, and 97853. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 97853 divided by the greatest perfect square from the list of all factors of 97853. We determined above that the greatest perfect square from the list of all factors of 97853 is 49. Furthermore, 97853 divided by 49 is 1997, therefore B equals 1997.

Now we have A and B and can get our answer to 97853 in its simplest radical form as follows:

√97853 = A√B

√97853 = 7√1997

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97853 to simplify the square root of 97853 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 97853 and then take the square root of that product. The prime factors that multiply together to make 97853 are 7 x 7 x 1997. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 97853 by the number (A) squared. 7 squared is 49 and 97853 divided by 49 is 1997. Therefore, B equals 1997.

Once again we have A and B and can get our answer to 97853 in its simplest radical form as follows:

√97853 = A√B

√97853 = 7√1997

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Simplify Square Root of 97854
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