Simplify Square Root of 39753

Here we will show you two methods that you can use to simplify the square root of 39753. In other words, we will show you how to find the square root of 39753 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.

√39753 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 39753 to simplify the square root of 39753. 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 39753. The factors of 39753 are 1, 3, 7, 9, 21, 63, 631, 1893, 4417, 5679, 13251, and 39753. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 39753 divided by the greatest perfect square from the list of all factors of 39753. We determined above that the greatest perfect square from the list of all factors of 39753 is 9. Furthermore, 39753 divided by 9 is 4417, therefore B equals 4417.

Now we have A and B and can get our answer to 39753 in its simplest radical form as follows:

√39753 = A√B

√39753 = 3√4417

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 39753 to simplify the square root of 39753 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 39753 and then take the square root of that product. The prime factors that multiply together to make 39753 are 3 x 3 x 7 x 631. 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 39753 by the number (A) squared. 3 squared is 9 and 39753 divided by 9 is 4417. Therefore, B equals 4417.

Once again we have A and B and can get our answer to 39753 in its simplest radical form as follows:

√39753 = A√B

√39753 = 3√4417

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Simplify Square Root of 39754
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