Simplify Square Root of 32050

Here we will show you two methods that you can use to simplify the square root of 32050. In other words, we will show you how to find the square root of 32050 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.

√32050 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32050 to simplify the square root of 32050. 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 32050. The factors of 32050 are 1, 2, 5, 10, 25, 50, 641, 1282, 3205, 6410, 16025, and 32050. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 32050 divided by the greatest perfect square from the list of all factors of 32050. We determined above that the greatest perfect square from the list of all factors of 32050 is 25. Furthermore, 32050 divided by 25 is 1282, therefore B equals 1282.

Now we have A and B and can get our answer to 32050 in its simplest radical form as follows:

√32050 = A√B

√32050 = 5√1282

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32050 to simplify the square root of 32050 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 32050 and then take the square root of that product. The prime factors that multiply together to make 32050 are 2 x 5 x 5 x 641. 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 32050 by the number (A) squared. 5 squared is 25 and 32050 divided by 25 is 1282. Therefore, B equals 1282.

Once again we have A and B and can get our answer to 32050 in its simplest radical form as follows:

√32050 = A√B

√32050 = 5√1282

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Simplify Square Root of 32051
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