Simplify Square Root of 74277

Here we will show you two methods that you can use to simplify the square root of 74277. In other words, we will show you how to find the square root of 74277 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.

√74277 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74277 to simplify the square root of 74277. 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 74277. The factors of 74277 are 1, 3, 7, 9, 21, 27, 63, 81, 131, 189, 393, 567, 917, 1179, 2751, 3537, 8253, 10611, 24759, and 74277. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 74277 divided by the greatest perfect square from the list of all factors of 74277. We determined above that the greatest perfect square from the list of all factors of 74277 is 81. Furthermore, 74277 divided by 81 is 917, therefore B equals 917.

Now we have A and B and can get our answer to 74277 in its simplest radical form as follows:

√74277 = A√B

√74277 = 9√917

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74277 to simplify the square root of 74277 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 74277 and then take the square root of that product. The prime factors that multiply together to make 74277 are 3 x 3 x 3 x 3 x 7 x 131. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 74277 by the number (A) squared. 9 squared is 81 and 74277 divided by 81 is 917. Therefore, B equals 917.

Once again we have A and B and can get our answer to 74277 in its simplest radical form as follows:

√74277 = A√B

√74277 = 9√917

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Simplify Square Root of 74278
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