Simplify Square Root of 5408

Here we will show you two methods that you can use to simplify the square root of 5408. In other words, we will show you how to find the square root of 5408 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.

√5408 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 5408 to simplify the square root of 5408. 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 5408. The factors of 5408 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 169, 208, 338, 416, 676, 1352, 2704, and 5408. Furthermore, the greatest perfect square on this list is 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Calculate 5408 divided by the greatest perfect square from the list of all factors of 5408. We determined above that the greatest perfect square from the list of all factors of 5408 is 2704. Furthermore, 5408 divided by 2704 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 5408 in its simplest radical form as follows:

√5408 = A√B

√5408 = 52√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 5408 to simplify the square root of 5408 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 5408 and then take the square root of that product. The prime factors that multiply together to make 5408 are 2 x 2 x 2 x 2 x 2 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 13 x 13 = 2704 and the square root of 2704 is 52. Therefore, A equals 52.

B = Divide 5408 by the number (A) squared. 52 squared is 2704 and 5408 divided by 2704 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 5408 in its simplest radical form as follows:

√5408 = A√B

√5408 = 52√2

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Simplify Square Root of 5409
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