Simplify Square Root of 74498

Here we will show you two methods that you can use to simplify the square root of 74498. In other words, we will show you how to find the square root of 74498 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.

√74498 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74498 to simplify the square root of 74498. 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 74498. The factors of 74498 are 1, 2, 193, 386, 37249, and 74498. Furthermore, the greatest perfect square on this list is 37249 and the square root of 37249 is 193. Therefore, A equals 193.

B = Calculate 74498 divided by the greatest perfect square from the list of all factors of 74498. We determined above that the greatest perfect square from the list of all factors of 74498 is 37249. Furthermore, 74498 divided by 37249 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 74498 in its simplest radical form as follows:

√74498 = A√B

√74498 = 193√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74498 to simplify the square root of 74498 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 74498 and then take the square root of that product. The prime factors that multiply together to make 74498 are 2 x 193 x 193. When we strip out the pairs only, we get 193 x 193 = 37249 and the square root of 37249 is 193. Therefore, A equals 193.

B = Divide 74498 by the number (A) squared. 193 squared is 37249 and 74498 divided by 37249 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 74498 in its simplest radical form as follows:

√74498 = A√B

√74498 = 193√2

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Simplify Square Root of 74499
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