Simplify Square Root of 84574

Here we will show you two methods that you can use to simplify the square root of 84574. In other words, we will show you how to find the square root of 84574 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.

√84574 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84574 to simplify the square root of 84574. 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 84574. The factors of 84574 are 1, 2, 7, 14, 49, 98, 863, 1726, 6041, 12082, 42287, and 84574. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 84574 divided by the greatest perfect square from the list of all factors of 84574. We determined above that the greatest perfect square from the list of all factors of 84574 is 49. Furthermore, 84574 divided by 49 is 1726, therefore B equals 1726.

Now we have A and B and can get our answer to 84574 in its simplest radical form as follows:

√84574 = A√B

√84574 = 7√1726

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84574 to simplify the square root of 84574 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 84574 and then take the square root of that product. The prime factors that multiply together to make 84574 are 2 x 7 x 7 x 863. 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 84574 by the number (A) squared. 7 squared is 49 and 84574 divided by 49 is 1726. Therefore, B equals 1726.

Once again we have A and B and can get our answer to 84574 in its simplest radical form as follows:

√84574 = A√B

√84574 = 7√1726

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Simplify Square Root of 84575
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