Simplify Square Root of 22445

Here we will show you two methods that you can use to simplify the square root of 22445. In other words, we will show you how to find the square root of 22445 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.

√22445 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22445 to simplify the square root of 22445. 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 22445. The factors of 22445 are 1, 5, 67, 335, 4489, and 22445. Furthermore, the greatest perfect square on this list is 4489 and the square root of 4489 is 67. Therefore, A equals 67.

B = Calculate 22445 divided by the greatest perfect square from the list of all factors of 22445. We determined above that the greatest perfect square from the list of all factors of 22445 is 4489. Furthermore, 22445 divided by 4489 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 22445 in its simplest radical form as follows:

√22445 = A√B

√22445 = 67√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22445 to simplify the square root of 22445 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 22445 and then take the square root of that product. The prime factors that multiply together to make 22445 are 5 x 67 x 67. When we strip out the pairs only, we get 67 x 67 = 4489 and the square root of 4489 is 67. Therefore, A equals 67.

B = Divide 22445 by the number (A) squared. 67 squared is 4489 and 22445 divided by 4489 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 22445 in its simplest radical form as follows:

√22445 = A√B

√22445 = 67√5

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Simplify Square Root of 22446
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