Simplify Square Root of 6962

Here we will show you two methods that you can use to simplify the square root of 6962. In other words, we will show you how to find the square root of 6962 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.

√6962 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 6962 to simplify the square root of 6962. 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 6962. The factors of 6962 are 1, 2, 59, 118, 3481, and 6962. Furthermore, the greatest perfect square on this list is 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Calculate 6962 divided by the greatest perfect square from the list of all factors of 6962. We determined above that the greatest perfect square from the list of all factors of 6962 is 3481. Furthermore, 6962 divided by 3481 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 6962 in its simplest radical form as follows:

√6962 = A√B

√6962 = 59√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 6962 to simplify the square root of 6962 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 6962 and then take the square root of that product. The prime factors that multiply together to make 6962 are 2 x 59 x 59. When we strip out the pairs only, we get 59 x 59 = 3481 and the square root of 3481 is 59. Therefore, A equals 59.

B = Divide 6962 by the number (A) squared. 59 squared is 3481 and 6962 divided by 3481 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 6962 in its simplest radical form as follows:

√6962 = A√B

√6962 = 59√2

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Simplify Square Root of 6963
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