Simplify Square Root of 940

Here we will show you two methods that you can use to simplify the square root of 940. In other words, we will show you how to find the square root of 940 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.

√940 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 940 to simplify the square root of 940. 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 940. The factors of 940 are 1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, and 940. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 940 divided by the greatest perfect square from the list of all factors of 940. We determined above that the greatest perfect square from the list of all factors of 940 is 4. Furthermore, 940 divided by 4 is 235, therefore B equals 235.

Now we have A and B and can get our answer to 940 in its simplest radical form as follows:

√940 = A√B

√940 = 2√235

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 940 to simplify the square root of 940 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 940 and then take the square root of that product. The prime factors that multiply together to make 940 are 2 x 2 x 5 x 47. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 940 by the number (A) squared. 2 squared is 4 and 940 divided by 4 is 235. Therefore, B equals 235.

Once again we have A and B and can get our answer to 940 in its simplest radical form as follows:

√940 = A√B

√940 = 2√235

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Simplify Square Root of 941
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