Simplify Square Root of 55451

Here we will show you two methods that you can use to simplify the square root of 55451. In other words, we will show you how to find the square root of 55451 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.

√55451 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55451 to simplify the square root of 55451. 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 55451. The factors of 55451 are 1, 11, 71, 781, 5041, and 55451. Furthermore, the greatest perfect square on this list is 5041 and the square root of 5041 is 71. Therefore, A equals 71.

B = Calculate 55451 divided by the greatest perfect square from the list of all factors of 55451. We determined above that the greatest perfect square from the list of all factors of 55451 is 5041. Furthermore, 55451 divided by 5041 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 55451 in its simplest radical form as follows:

√55451 = A√B

√55451 = 71√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55451 to simplify the square root of 55451 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 55451 and then take the square root of that product. The prime factors that multiply together to make 55451 are 11 x 71 x 71. When we strip out the pairs only, we get 71 x 71 = 5041 and the square root of 5041 is 71. Therefore, A equals 71.

B = Divide 55451 by the number (A) squared. 71 squared is 5041 and 55451 divided by 5041 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 55451 in its simplest radical form as follows:

√55451 = A√B

√55451 = 71√11

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Simplify Square Root of 55452
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