Simplify Square Root of 9850

Here we will show you two methods that you can use to simplify the square root of 9850. In other words, we will show you how to find the square root of 9850 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.

√9850 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9850 to simplify the square root of 9850. 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 9850. The factors of 9850 are 1, 2, 5, 10, 25, 50, 197, 394, 985, 1970, 4925, and 9850. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 9850 divided by the greatest perfect square from the list of all factors of 9850. We determined above that the greatest perfect square from the list of all factors of 9850 is 25. Furthermore, 9850 divided by 25 is 394, therefore B equals 394.

Now we have A and B and can get our answer to 9850 in its simplest radical form as follows:

√9850 = A√B

√9850 = 5√394

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9850 to simplify the square root of 9850 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 9850 and then take the square root of that product. The prime factors that multiply together to make 9850 are 2 x 5 x 5 x 197. 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 9850 by the number (A) squared. 5 squared is 25 and 9850 divided by 25 is 394. Therefore, B equals 394.

Once again we have A and B and can get our answer to 9850 in its simplest radical form as follows:

√9850 = A√B

√9850 = 5√394

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Simplify Square Root of 9851
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