Simplify Square Root of 49650

Here we will show you two methods that you can use to simplify the square root of 49650. In other words, we will show you how to find the square root of 49650 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.

√49650 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49650 to simplify the square root of 49650. 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 49650. The factors of 49650 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150, 331, 662, 993, 1655, 1986, 3310, 4965, 8275, 9930, 16550, 24825, and 49650. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 49650 divided by the greatest perfect square from the list of all factors of 49650. We determined above that the greatest perfect square from the list of all factors of 49650 is 25. Furthermore, 49650 divided by 25 is 1986, therefore B equals 1986.

Now we have A and B and can get our answer to 49650 in its simplest radical form as follows:

√49650 = A√B

√49650 = 5√1986

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49650 to simplify the square root of 49650 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 49650 and then take the square root of that product. The prime factors that multiply together to make 49650 are 2 x 3 x 5 x 5 x 331. 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 49650 by the number (A) squared. 5 squared is 25 and 49650 divided by 25 is 1986. Therefore, B equals 1986.

Once again we have A and B and can get our answer to 49650 in its simplest radical form as follows:

√49650 = A√B

√49650 = 5√1986

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Simplify Square Root of 49651
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