Simplify Square Root of 55675

Here we will show you two methods that you can use to simplify the square root of 55675. In other words, we will show you how to find the square root of 55675 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.

√55675 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55675 to simplify the square root of 55675. 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 55675. The factors of 55675 are 1, 5, 17, 25, 85, 131, 425, 655, 2227, 3275, 11135, and 55675. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 55675 divided by the greatest perfect square from the list of all factors of 55675. We determined above that the greatest perfect square from the list of all factors of 55675 is 25. Furthermore, 55675 divided by 25 is 2227, therefore B equals 2227.

Now we have A and B and can get our answer to 55675 in its simplest radical form as follows:

√55675 = A√B

√55675 = 5√2227

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55675 to simplify the square root of 55675 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 55675 and then take the square root of that product. The prime factors that multiply together to make 55675 are 5 x 5 x 17 x 131. 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 55675 by the number (A) squared. 5 squared is 25 and 55675 divided by 25 is 2227. Therefore, B equals 2227.

Once again we have A and B and can get our answer to 55675 in its simplest radical form as follows:

√55675 = A√B

√55675 = 5√2227

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Simplify Square Root of 55676
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