Simplify Square Root of 74849

Here we will show you two methods that you can use to simplify the square root of 74849. In other words, we will show you how to find the square root of 74849 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.

√74849 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74849 to simplify the square root of 74849. 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 74849. The factors of 74849 are 1, 29, 89, 841, 2581, and 74849. Furthermore, the greatest perfect square on this list is 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Calculate 74849 divided by the greatest perfect square from the list of all factors of 74849. We determined above that the greatest perfect square from the list of all factors of 74849 is 841. Furthermore, 74849 divided by 841 is 89, therefore B equals 89.

Now we have A and B and can get our answer to 74849 in its simplest radical form as follows:

√74849 = A√B

√74849 = 29√89

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74849 to simplify the square root of 74849 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 74849 and then take the square root of that product. The prime factors that multiply together to make 74849 are 29 x 29 x 89. When we strip out the pairs only, we get 29 x 29 = 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Divide 74849 by the number (A) squared. 29 squared is 841 and 74849 divided by 841 is 89. Therefore, B equals 89.

Once again we have A and B and can get our answer to 74849 in its simplest radical form as follows:

√74849 = A√B

√74849 = 29√89

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Simplify Square Root of 74850
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