Simplify Square Root of 71150

Here we will show you two methods that you can use to simplify the square root of 71150. In other words, we will show you how to find the square root of 71150 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.

√71150 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 71150 to simplify the square root of 71150. 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 71150. The factors of 71150 are 1, 2, 5, 10, 25, 50, 1423, 2846, 7115, 14230, 35575, and 71150. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 71150 divided by the greatest perfect square from the list of all factors of 71150. We determined above that the greatest perfect square from the list of all factors of 71150 is 25. Furthermore, 71150 divided by 25 is 2846, therefore B equals 2846.

Now we have A and B and can get our answer to 71150 in its simplest radical form as follows:

√71150 = A√B

√71150 = 5√2846

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 71150 to simplify the square root of 71150 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 71150 and then take the square root of that product. The prime factors that multiply together to make 71150 are 2 x 5 x 5 x 1423. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 71150 by the number (A) squared. 5 squared is 25 and 71150 divided by 25 is 2846. Therefore, B equals 2846.

Once again we have A and B and can get our answer to 71150 in its simplest radical form as follows:

√71150 = A√B

√71150 = 5√2846

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Simplify Square Root of 71151
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