Simplify Square Root of 75425

Here we will show you two methods that you can use to simplify the square root of 75425. In other words, we will show you how to find the square root of 75425 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.

√75425 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75425 to simplify the square root of 75425. 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 75425. The factors of 75425 are 1, 5, 7, 25, 35, 175, 431, 2155, 3017, 10775, 15085, and 75425. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 75425 divided by the greatest perfect square from the list of all factors of 75425. We determined above that the greatest perfect square from the list of all factors of 75425 is 25. Furthermore, 75425 divided by 25 is 3017, therefore B equals 3017.

Now we have A and B and can get our answer to 75425 in its simplest radical form as follows:

√75425 = A√B

√75425 = 5√3017

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75425 to simplify the square root of 75425 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 75425 and then take the square root of that product. The prime factors that multiply together to make 75425 are 5 x 5 x 7 x 431. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 75425 by the number (A) squared. 5 squared is 25 and 75425 divided by 25 is 3017. Therefore, B equals 3017.

Once again we have A and B and can get our answer to 75425 in its simplest radical form as follows:

√75425 = A√B

√75425 = 5√3017

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Simplify Square Root of 75426
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