Simplify Square Root of 75746

Here we will show you two methods that you can use to simplify the square root of 75746. In other words, we will show you how to find the square root of 75746 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.

√75746 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75746 to simplify the square root of 75746. 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 75746. The factors of 75746 are 1, 2, 11, 22, 121, 242, 313, 626, 3443, 6886, 37873, and 75746. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 75746 divided by the greatest perfect square from the list of all factors of 75746. We determined above that the greatest perfect square from the list of all factors of 75746 is 121. Furthermore, 75746 divided by 121 is 626, therefore B equals 626.

Now we have A and B and can get our answer to 75746 in its simplest radical form as follows:

√75746 = A√B

√75746 = 11√626

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75746 to simplify the square root of 75746 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 75746 and then take the square root of that product. The prime factors that multiply together to make 75746 are 2 x 11 x 11 x 313. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 75746 by the number (A) squared. 11 squared is 121 and 75746 divided by 121 is 626. Therefore, B equals 626.

Once again we have A and B and can get our answer to 75746 in its simplest radical form as follows:

√75746 = A√B

√75746 = 11√626

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Simplify Square Root of 75747
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