Simplify Square Root of 15775

Here we will show you two methods that you can use to simplify the square root of 15775. In other words, we will show you how to find the square root of 15775 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.

√15775 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15775 to simplify the square root of 15775. 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 15775. The factors of 15775 are 1, 5, 25, 631, 3155, and 15775. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 15775 divided by the greatest perfect square from the list of all factors of 15775. We determined above that the greatest perfect square from the list of all factors of 15775 is 25. Furthermore, 15775 divided by 25 is 631, therefore B equals 631.

Now we have A and B and can get our answer to 15775 in its simplest radical form as follows:

√15775 = A√B

√15775 = 5√631

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15775 to simplify the square root of 15775 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 15775 and then take the square root of that product. The prime factors that multiply together to make 15775 are 5 x 5 x 631. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 15775 by the number (A) squared. 5 squared is 25 and 15775 divided by 25 is 631. Therefore, B equals 631.

Once again we have A and B and can get our answer to 15775 in its simplest radical form as follows:

√15775 = A√B

√15775 = 5√631

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Simplify Square Root of 15776
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