Simplify Square Root of 7844

Here we will show you two methods that you can use to simplify the square root of 7844. In other words, we will show you how to find the square root of 7844 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.

√7844 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7844 to simplify the square root of 7844. 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 7844. The factors of 7844 are 1, 2, 4, 37, 53, 74, 106, 148, 212, 1961, 3922, and 7844. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 7844 divided by the greatest perfect square from the list of all factors of 7844. We determined above that the greatest perfect square from the list of all factors of 7844 is 4. Furthermore, 7844 divided by 4 is 1961, therefore B equals 1961.

Now we have A and B and can get our answer to 7844 in its simplest radical form as follows:

√7844 = A√B

√7844 = 2√1961

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7844 to simplify the square root of 7844 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 7844 and then take the square root of that product. The prime factors that multiply together to make 7844 are 2 x 2 x 37 x 53. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 7844 by the number (A) squared. 2 squared is 4 and 7844 divided by 4 is 1961. Therefore, B equals 1961.

Once again we have A and B and can get our answer to 7844 in its simplest radical form as follows:

√7844 = A√B

√7844 = 2√1961

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Simplify Square Root of 7845
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