Simplify Square Root of 34902

Here we will show you two methods that you can use to simplify the square root of 34902. In other words, we will show you how to find the square root of 34902 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.

√34902 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34902 to simplify the square root of 34902. 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 34902. The factors of 34902 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 277, 554, 831, 1662, 1939, 2493, 3878, 4986, 5817, 11634, 17451, and 34902. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 34902 divided by the greatest perfect square from the list of all factors of 34902. We determined above that the greatest perfect square from the list of all factors of 34902 is 9. Furthermore, 34902 divided by 9 is 3878, therefore B equals 3878.

Now we have A and B and can get our answer to 34902 in its simplest radical form as follows:

√34902 = A√B

√34902 = 3√3878

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34902 to simplify the square root of 34902 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 34902 and then take the square root of that product. The prime factors that multiply together to make 34902 are 2 x 3 x 3 x 7 x 277. 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 34902 by the number (A) squared. 3 squared is 9 and 34902 divided by 9 is 3878. Therefore, B equals 3878.

Once again we have A and B and can get our answer to 34902 in its simplest radical form as follows:

√34902 = A√B

√34902 = 3√3878

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Simplify Square Root of 34903
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