Simplify Square Root of 15453

Here we will show you two methods that you can use to simplify the square root of 15453. In other words, we will show you how to find the square root of 15453 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.

√15453 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15453 to simplify the square root of 15453. 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 15453. The factors of 15453 are 1, 3, 9, 17, 51, 101, 153, 303, 909, 1717, 5151, and 15453. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 15453 divided by the greatest perfect square from the list of all factors of 15453. We determined above that the greatest perfect square from the list of all factors of 15453 is 9. Furthermore, 15453 divided by 9 is 1717, therefore B equals 1717.

Now we have A and B and can get our answer to 15453 in its simplest radical form as follows:

√15453 = A√B

√15453 = 3√1717

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15453 to simplify the square root of 15453 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 15453 and then take the square root of that product. The prime factors that multiply together to make 15453 are 3 x 3 x 17 x 101. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 15453 by the number (A) squared. 3 squared is 9 and 15453 divided by 9 is 1717. Therefore, B equals 1717.

Once again we have A and B and can get our answer to 15453 in its simplest radical form as follows:

√15453 = A√B

√15453 = 3√1717

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Simplify Square Root of 15454
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