Simplify Square Root of 549

Here we will show you two methods that you can use to simplify the square root of 549. In other words, we will show you how to find the square root of 549 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.

√549 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 549 to simplify the square root of 549. 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 549. The factors of 549 are 1, 3, 9, 61, 183, and 549. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 549 divided by the greatest perfect square from the list of all factors of 549. We determined above that the greatest perfect square from the list of all factors of 549 is 9. Furthermore, 549 divided by 9 is 61, therefore B equals 61.

Now we have A and B and can get our answer to 549 in its simplest radical form as follows:

√549 = A√B

√549 = 3√61

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 549 to simplify the square root of 549 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 549 and then take the square root of that product. The prime factors that multiply together to make 549 are 3 x 3 x 61. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 549 by the number (A) squared. 3 squared is 9 and 549 divided by 9 is 61. Therefore, B equals 61.

Once again we have A and B and can get our answer to 549 in its simplest radical form as follows:

√549 = A√B

√549 = 3√61

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Simplify Square Root of 550
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