Simplify Square Root of 29340

Here we will show you two methods that you can use to simplify the square root of 29340. In other words, we will show you how to find the square root of 29340 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.

√29340 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 29340 to simplify the square root of 29340. 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 29340. The factors of 29340 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 163, 180, 326, 489, 652, 815, 978, 1467, 1630, 1956, 2445, 2934, 3260, 4890, 5868, 7335, 9780, 14670, and 29340. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 29340 divided by the greatest perfect square from the list of all factors of 29340. We determined above that the greatest perfect square from the list of all factors of 29340 is 36. Furthermore, 29340 divided by 36 is 815, therefore B equals 815.

Now we have A and B and can get our answer to 29340 in its simplest radical form as follows:

√29340 = A√B

√29340 = 6√815

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 29340 to simplify the square root of 29340 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 29340 and then take the square root of that product. The prime factors that multiply together to make 29340 are 2 x 2 x 3 x 3 x 5 x 163. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 29340 by the number (A) squared. 6 squared is 36 and 29340 divided by 36 is 815. Therefore, B equals 815.

Once again we have A and B and can get our answer to 29340 in its simplest radical form as follows:

√29340 = A√B

√29340 = 6√815

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