Simplify Square Root of 15851

Here we will show you two methods that you can use to simplify the square root of 15851. In other words, we will show you how to find the square root of 15851 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.

√15851 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15851 to simplify the square root of 15851. 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 15851. The factors of 15851 are 1, 11, 121, 131, 1441, and 15851. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 15851 divided by the greatest perfect square from the list of all factors of 15851. We determined above that the greatest perfect square from the list of all factors of 15851 is 121. Furthermore, 15851 divided by 121 is 131, therefore B equals 131.

Now we have A and B and can get our answer to 15851 in its simplest radical form as follows:

√15851 = A√B

√15851 = 11√131

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15851 to simplify the square root of 15851 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 15851 and then take the square root of that product. The prime factors that multiply together to make 15851 are 11 x 11 x 131. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 15851 by the number (A) squared. 11 squared is 121 and 15851 divided by 121 is 131. Therefore, B equals 131.

Once again we have A and B and can get our answer to 15851 in its simplest radical form as follows:

√15851 = A√B

√15851 = 11√131

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Simplify Square Root of 15852
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