Simplify Square Root of 54702

Here we will show you two methods that you can use to simplify the square root of 54702. In other words, we will show you how to find the square root of 54702 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.

√54702 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54702 to simplify the square root of 54702. 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 54702. The factors of 54702 are 1, 2, 3, 6, 9, 18, 27, 54, 1013, 2026, 3039, 6078, 9117, 18234, 27351, and 54702. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 54702 divided by the greatest perfect square from the list of all factors of 54702. We determined above that the greatest perfect square from the list of all factors of 54702 is 9. Furthermore, 54702 divided by 9 is 6078, therefore B equals 6078.

Now we have A and B and can get our answer to 54702 in its simplest radical form as follows:

√54702 = A√B

√54702 = 3√6078

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54702 to simplify the square root of 54702 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 54702 and then take the square root of that product. The prime factors that multiply together to make 54702 are 2 x 3 x 3 x 3 x 1013. 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 54702 by the number (A) squared. 3 squared is 9 and 54702 divided by 9 is 6078. Therefore, B equals 6078.

Once again we have A and B and can get our answer to 54702 in its simplest radical form as follows:

√54702 = A√B

√54702 = 3√6078

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Simplify Square Root of 54703
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