Simplify Square Root of 78141

Here we will show you two methods that you can use to simplify the square root of 78141. In other words, we will show you how to find the square root of 78141 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.

√78141 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78141 to simplify the square root of 78141. 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 78141. The factors of 78141 are 1, 3, 7, 21, 61, 183, 427, 1281, 3721, 11163, 26047, and 78141. Furthermore, the greatest perfect square on this list is 3721 and the square root of 3721 is 61. Therefore, A equals 61.

B = Calculate 78141 divided by the greatest perfect square from the list of all factors of 78141. We determined above that the greatest perfect square from the list of all factors of 78141 is 3721. Furthermore, 78141 divided by 3721 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 78141 in its simplest radical form as follows:

√78141 = A√B

√78141 = 61√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78141 to simplify the square root of 78141 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 78141 and then take the square root of that product. The prime factors that multiply together to make 78141 are 3 x 7 x 61 x 61. When we strip out the pairs only, we get 61 x 61 = 3721 and the square root of 3721 is 61. Therefore, A equals 61.

B = Divide 78141 by the number (A) squared. 61 squared is 3721 and 78141 divided by 3721 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 78141 in its simplest radical form as follows:

√78141 = A√B

√78141 = 61√21

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Simplify Square Root of 78142
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