Simplify Square Root of 548

Here we will show you two methods that you can use to simplify the square root of 548. In other words, we will show you how to find the square root of 548 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.

√548 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 548 to simplify the square root of 548. 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 548. The factors of 548 are 1, 2, 4, 137, 274, and 548. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 548 divided by the greatest perfect square from the list of all factors of 548. We determined above that the greatest perfect square from the list of all factors of 548 is 4. Furthermore, 548 divided by 4 is 137, therefore B equals 137.

Now we have A and B and can get our answer to 548 in its simplest radical form as follows:

√548 = A√B

√548 = 2√137

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 548 to simplify the square root of 548 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 548 and then take the square root of that product. The prime factors that multiply together to make 548 are 2 x 2 x 137. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 548 by the number (A) squared. 2 squared is 4 and 548 divided by 4 is 137. Therefore, B equals 137.

Once again we have A and B and can get our answer to 548 in its simplest radical form as follows:

√548 = A√B

√548 = 2√137

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Simplify Square Root of 549
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