Simplify Square Root of 45177

Here we will show you two methods that you can use to simplify the square root of 45177. In other words, we will show you how to find the square root of 45177 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.

√45177 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45177 to simplify the square root of 45177. 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 45177. The factors of 45177 are 1, 3, 11, 33, 37, 111, 407, 1221, 1369, 4107, 15059, and 45177. Furthermore, the greatest perfect square on this list is 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Calculate 45177 divided by the greatest perfect square from the list of all factors of 45177. We determined above that the greatest perfect square from the list of all factors of 45177 is 1369. Furthermore, 45177 divided by 1369 is 33, therefore B equals 33.

Now we have A and B and can get our answer to 45177 in its simplest radical form as follows:

√45177 = A√B

√45177 = 37√33

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45177 to simplify the square root of 45177 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 45177 and then take the square root of that product. The prime factors that multiply together to make 45177 are 3 x 11 x 37 x 37. When we strip out the pairs only, we get 37 x 37 = 1369 and the square root of 1369 is 37. Therefore, A equals 37.

B = Divide 45177 by the number (A) squared. 37 squared is 1369 and 45177 divided by 1369 is 33. Therefore, B equals 33.

Once again we have A and B and can get our answer to 45177 in its simplest radical form as follows:

√45177 = A√B

√45177 = 37√33

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