Simplify Square Root of 75843

Here we will show you two methods that you can use to simplify the square root of 75843. In other words, we will show you how to find the square root of 75843 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.

√75843 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75843 to simplify the square root of 75843. 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 75843. The factors of 75843 are 1, 3, 9, 27, 53, 159, 477, 1431, 2809, 8427, 25281, and 75843. Furthermore, the greatest perfect square on this list is 25281 and the square root of 25281 is 159. Therefore, A equals 159.

B = Calculate 75843 divided by the greatest perfect square from the list of all factors of 75843. We determined above that the greatest perfect square from the list of all factors of 75843 is 25281. Furthermore, 75843 divided by 25281 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 75843 in its simplest radical form as follows:

√75843 = A√B

√75843 = 159√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75843 to simplify the square root of 75843 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 75843 and then take the square root of that product. The prime factors that multiply together to make 75843 are 3 x 3 x 3 x 53 x 53. When we strip out the pairs only, we get 3 x 3 x 53 x 53 = 25281 and the square root of 25281 is 159. Therefore, A equals 159.

B = Divide 75843 by the number (A) squared. 159 squared is 25281 and 75843 divided by 25281 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 75843 in its simplest radical form as follows:

√75843 = A√B

√75843 = 159√3

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Simplify Square Root of 75844
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