Simplify Square Root of 7038

Here we will show you two methods that you can use to simplify the square root of 7038. In other words, we will show you how to find the square root of 7038 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.

√7038 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7038 to simplify the square root of 7038. 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 7038. The factors of 7038 are 1, 2, 3, 6, 9, 17, 18, 23, 34, 46, 51, 69, 102, 138, 153, 207, 306, 391, 414, 782, 1173, 2346, 3519, and 7038. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 7038 divided by the greatest perfect square from the list of all factors of 7038. We determined above that the greatest perfect square from the list of all factors of 7038 is 9. Furthermore, 7038 divided by 9 is 782, therefore B equals 782.

Now we have A and B and can get our answer to 7038 in its simplest radical form as follows:

√7038 = A√B

√7038 = 3√782

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7038 to simplify the square root of 7038 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 7038 and then take the square root of that product. The prime factors that multiply together to make 7038 are 2 x 3 x 3 x 17 x 23. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 7038 by the number (A) squared. 3 squared is 9 and 7038 divided by 9 is 782. Therefore, B equals 782.

Once again we have A and B and can get our answer to 7038 in its simplest radical form as follows:

√7038 = A√B

√7038 = 3√782

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Simplify Square Root of 7039
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