Simplify Square Root of 99458

Here we will show you two methods that you can use to simplify the square root of 99458. In other words, we will show you how to find the square root of 99458 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.

√99458 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 99458 to simplify the square root of 99458. 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 99458. The factors of 99458 are 1, 2, 223, 446, 49729, and 99458. Furthermore, the greatest perfect square on this list is 49729 and the square root of 49729 is 223. Therefore, A equals 223.

B = Calculate 99458 divided by the greatest perfect square from the list of all factors of 99458. We determined above that the greatest perfect square from the list of all factors of 99458 is 49729. Furthermore, 99458 divided by 49729 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 99458 in its simplest radical form as follows:

√99458 = A√B

√99458 = 223√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 99458 to simplify the square root of 99458 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 99458 and then take the square root of that product. The prime factors that multiply together to make 99458 are 2 x 223 x 223. When we strip out the pairs only, we get 223 x 223 = 49729 and the square root of 49729 is 223. Therefore, A equals 223.

B = Divide 99458 by the number (A) squared. 223 squared is 49729 and 99458 divided by 49729 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 99458 in its simplest radical form as follows:

√99458 = A√B

√99458 = 223√2

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Simplify Square Root of 99459
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