Simplify Square Root of 34398

Here we will show you two methods that you can use to simplify the square root of 34398. In other words, we will show you how to find the square root of 34398 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.

√34398 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 34398 to simplify the square root of 34398. 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 34398. The factors of 34398 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 49, 54, 63, 78, 91, 98, 117, 126, 147, 182, 189, 234, 273, 294, 351, 378, 441, 546, 637, 702, 819, 882, 1274, 1323, 1638, 1911, 2457, 2646, 3822, 4914, 5733, 11466, 17199, and 34398. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 34398 divided by the greatest perfect square from the list of all factors of 34398. We determined above that the greatest perfect square from the list of all factors of 34398 is 441. Furthermore, 34398 divided by 441 is 78, therefore B equals 78.

Now we have A and B and can get our answer to 34398 in its simplest radical form as follows:

√34398 = A√B

√34398 = 21√78

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 34398 to simplify the square root of 34398 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 34398 and then take the square root of that product. The prime factors that multiply together to make 34398 are 2 x 3 x 3 x 3 x 7 x 7 x 13. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 34398 by the number (A) squared. 21 squared is 441 and 34398 divided by 441 is 78. Therefore, B equals 78.

Once again we have A and B and can get our answer to 34398 in its simplest radical form as follows:

√34398 = A√B

√34398 = 21√78

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