Simplify Square Root of 69628

Here we will show you two methods that you can use to simplify the square root of 69628. In other words, we will show you how to find the square root of 69628 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.

√69628 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69628 to simplify the square root of 69628. 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 69628. The factors of 69628 are 1, 2, 4, 13, 26, 52, 103, 169, 206, 338, 412, 676, 1339, 2678, 5356, 17407, 34814, and 69628. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 69628 divided by the greatest perfect square from the list of all factors of 69628. We determined above that the greatest perfect square from the list of all factors of 69628 is 676. Furthermore, 69628 divided by 676 is 103, therefore B equals 103.

Now we have A and B and can get our answer to 69628 in its simplest radical form as follows:

√69628 = A√B

√69628 = 26√103

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69628 to simplify the square root of 69628 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 69628 and then take the square root of that product. The prime factors that multiply together to make 69628 are 2 x 2 x 13 x 13 x 103. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 69628 by the number (A) squared. 26 squared is 676 and 69628 divided by 676 is 103. Therefore, B equals 103.

Once again we have A and B and can get our answer to 69628 in its simplest radical form as follows:

√69628 = A√B

√69628 = 26√103

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Simplify Square Root of 69629
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