Simplify Square Root of 44402

Here we will show you two methods that you can use to simplify the square root of 44402. In other words, we will show you how to find the square root of 44402 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.

√44402 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 44402 to simplify the square root of 44402. 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 44402. The factors of 44402 are 1, 2, 149, 298, 22201, and 44402. Furthermore, the greatest perfect square on this list is 22201 and the square root of 22201 is 149. Therefore, A equals 149.

B = Calculate 44402 divided by the greatest perfect square from the list of all factors of 44402. We determined above that the greatest perfect square from the list of all factors of 44402 is 22201. Furthermore, 44402 divided by 22201 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 44402 in its simplest radical form as follows:

√44402 = A√B

√44402 = 149√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 44402 to simplify the square root of 44402 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 44402 and then take the square root of that product. The prime factors that multiply together to make 44402 are 2 x 149 x 149. When we strip out the pairs only, we get 149 x 149 = 22201 and the square root of 22201 is 149. Therefore, A equals 149.

B = Divide 44402 by the number (A) squared. 149 squared is 22201 and 44402 divided by 22201 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 44402 in its simplest radical form as follows:

√44402 = A√B

√44402 = 149√2

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Simplify Square Root of 44403
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