Simplify Square Root of 21294

Here we will show you two methods that you can use to simplify the square root of 21294. In other words, we will show you how to find the square root of 21294 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.

√21294 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21294 to simplify the square root of 21294. 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 21294. The factors of 21294 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91, 117, 126, 169, 182, 234, 273, 338, 507, 546, 819, 1014, 1183, 1521, 1638, 2366, 3042, 3549, 7098, 10647, and 21294. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 21294 divided by the greatest perfect square from the list of all factors of 21294. We determined above that the greatest perfect square from the list of all factors of 21294 is 1521. Furthermore, 21294 divided by 1521 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 21294 in its simplest radical form as follows:

√21294 = A√B

√21294 = 39√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21294 to simplify the square root of 21294 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 21294 and then take the square root of that product. The prime factors that multiply together to make 21294 are 2 x 3 x 3 x 7 x 13 x 13. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 21294 by the number (A) squared. 39 squared is 1521 and 21294 divided by 1521 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 21294 in its simplest radical form as follows:

√21294 = A√B

√21294 = 39√14

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