Simplify Square Root of 49275

Here we will show you two methods that you can use to simplify the square root of 49275. In other words, we will show you how to find the square root of 49275 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.

√49275 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49275 to simplify the square root of 49275. 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 49275. The factors of 49275 are 1, 3, 5, 9, 15, 25, 27, 45, 73, 75, 135, 219, 225, 365, 657, 675, 1095, 1825, 1971, 3285, 5475, 9855, 16425, and 49275. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 49275 divided by the greatest perfect square from the list of all factors of 49275. We determined above that the greatest perfect square from the list of all factors of 49275 is 225. Furthermore, 49275 divided by 225 is 219, therefore B equals 219.

Now we have A and B and can get our answer to 49275 in its simplest radical form as follows:

√49275 = A√B

√49275 = 15√219

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49275 to simplify the square root of 49275 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 49275 and then take the square root of that product. The prime factors that multiply together to make 49275 are 3 x 3 x 3 x 5 x 5 x 73. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 49275 by the number (A) squared. 15 squared is 225 and 49275 divided by 225 is 219. Therefore, B equals 219.

Once again we have A and B and can get our answer to 49275 in its simplest radical form as follows:

√49275 = A√B

√49275 = 15√219

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Simplify Square Root of 49276
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