Simplify Square Root of 9800

Here we will show you two methods that you can use to simplify the square root of 9800. In other words, we will show you how to find the square root of 9800 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.

√9800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9800 to simplify the square root of 9800. 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 9800. The factors of 9800 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 49, 50, 56, 70, 98, 100, 140, 175, 196, 200, 245, 280, 350, 392, 490, 700, 980, 1225, 1400, 1960, 2450, 4900, and 9800. Furthermore, the greatest perfect square on this list is 4900 and the square root of 4900 is 70. Therefore, A equals 70.

B = Calculate 9800 divided by the greatest perfect square from the list of all factors of 9800. We determined above that the greatest perfect square from the list of all factors of 9800 is 4900. Furthermore, 9800 divided by 4900 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 9800 in its simplest radical form as follows:

√9800 = A√B

√9800 = 70√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9800 to simplify the square root of 9800 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 9800 and then take the square root of that product. The prime factors that multiply together to make 9800 are 2 x 2 x 2 x 5 x 5 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 7 x 7 = 4900 and the square root of 4900 is 70. Therefore, A equals 70.

B = Divide 9800 by the number (A) squared. 70 squared is 4900 and 9800 divided by 4900 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 9800 in its simplest radical form as follows:

√9800 = A√B

√9800 = 70√2

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Simplify Square Root of 9801
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