Simplify Square Root of 7448

Here we will show you two methods that you can use to simplify the square root of 7448. In other words, we will show you how to find the square root of 7448 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.

√7448 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7448 to simplify the square root of 7448. 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 7448. The factors of 7448 are 1, 2, 4, 7, 8, 14, 19, 28, 38, 49, 56, 76, 98, 133, 152, 196, 266, 392, 532, 931, 1064, 1862, 3724, and 7448. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 7448 divided by the greatest perfect square from the list of all factors of 7448. We determined above that the greatest perfect square from the list of all factors of 7448 is 196. Furthermore, 7448 divided by 196 is 38, therefore B equals 38.

Now we have A and B and can get our answer to 7448 in its simplest radical form as follows:

√7448 = A√B

√7448 = 14√38

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7448 to simplify the square root of 7448 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 7448 and then take the square root of that product. The prime factors that multiply together to make 7448 are 2 x 2 x 2 x 7 x 7 x 19. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 7448 by the number (A) squared. 14 squared is 196 and 7448 divided by 196 is 38. Therefore, B equals 38.

Once again we have A and B and can get our answer to 7448 in its simplest radical form as follows:

√7448 = A√B

√7448 = 14√38

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Simplify Square Root of 7449
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