Simplify Square Root of 75449

Here we will show you two methods that you can use to simplify the square root of 75449. In other words, we will show you how to find the square root of 75449 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.

√75449 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75449 to simplify the square root of 75449. 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 75449. The factors of 75449 are 1, 11, 19, 209, 361, 3971, 6859, and 75449. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 75449 divided by the greatest perfect square from the list of all factors of 75449. We determined above that the greatest perfect square from the list of all factors of 75449 is 361. Furthermore, 75449 divided by 361 is 209, therefore B equals 209.

Now we have A and B and can get our answer to 75449 in its simplest radical form as follows:

√75449 = A√B

√75449 = 19√209

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75449 to simplify the square root of 75449 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 75449 and then take the square root of that product. The prime factors that multiply together to make 75449 are 11 x 19 x 19 x 19. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 75449 by the number (A) squared. 19 squared is 361 and 75449 divided by 361 is 209. Therefore, B equals 209.

Once again we have A and B and can get our answer to 75449 in its simplest radical form as follows:

√75449 = A√B

√75449 = 19√209

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Simplify Square Root of 75450
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