Simplify Square Root of 53428

Here we will show you two methods that you can use to simplify the square root of 53428. In other words, we will show you how to find the square root of 53428 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.

√53428 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53428 to simplify the square root of 53428. 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 53428. The factors of 53428 are 1, 2, 4, 19, 37, 38, 74, 76, 148, 361, 703, 722, 1406, 1444, 2812, 13357, 26714, and 53428. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 53428 divided by the greatest perfect square from the list of all factors of 53428. We determined above that the greatest perfect square from the list of all factors of 53428 is 1444. Furthermore, 53428 divided by 1444 is 37, therefore B equals 37.

Now we have A and B and can get our answer to 53428 in its simplest radical form as follows:

√53428 = A√B

√53428 = 38√37

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53428 to simplify the square root of 53428 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 53428 and then take the square root of that product. The prime factors that multiply together to make 53428 are 2 x 2 x 19 x 19 x 37. When we strip out the pairs only, we get 2 x 2 x 19 x 19 = 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Divide 53428 by the number (A) squared. 38 squared is 1444 and 53428 divided by 1444 is 37. Therefore, B equals 37.

Once again we have A and B and can get our answer to 53428 in its simplest radical form as follows:

√53428 = A√B

√53428 = 38√37

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Simplify Square Root of 53429
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