Simplify Square Root of 15842

Here we will show you two methods that you can use to simplify the square root of 15842. In other words, we will show you how to find the square root of 15842 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.

√15842 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15842 to simplify the square root of 15842. 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 15842. The factors of 15842 are 1, 2, 89, 178, 7921, and 15842. Furthermore, the greatest perfect square on this list is 7921 and the square root of 7921 is 89. Therefore, A equals 89.

B = Calculate 15842 divided by the greatest perfect square from the list of all factors of 15842. We determined above that the greatest perfect square from the list of all factors of 15842 is 7921. Furthermore, 15842 divided by 7921 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 15842 in its simplest radical form as follows:

√15842 = A√B

√15842 = 89√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15842 to simplify the square root of 15842 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 15842 and then take the square root of that product. The prime factors that multiply together to make 15842 are 2 x 89 x 89. When we strip out the pairs only, we get 89 x 89 = 7921 and the square root of 7921 is 89. Therefore, A equals 89.

B = Divide 15842 by the number (A) squared. 89 squared is 7921 and 15842 divided by 7921 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 15842 in its simplest radical form as follows:

√15842 = A√B

√15842 = 89√2

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Simplify Square Root of 15843
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