Simplify Square Root of 4840

Here we will show you two methods that you can use to simplify the square root of 4840. In other words, we will show you how to find the square root of 4840 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.

√4840 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 4840 to simplify the square root of 4840. 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 4840. The factors of 4840 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 121, 220, 242, 440, 484, 605, 968, 1210, 2420, and 4840. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 4840 divided by the greatest perfect square from the list of all factors of 4840. We determined above that the greatest perfect square from the list of all factors of 4840 is 484. Furthermore, 4840 divided by 484 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 4840 in its simplest radical form as follows:

√4840 = A√B

√4840 = 22√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 4840 to simplify the square root of 4840 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 4840 and then take the square root of that product. The prime factors that multiply together to make 4840 are 2 x 2 x 2 x 5 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 4840 by the number (A) squared. 22 squared is 484 and 4840 divided by 484 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 4840 in its simplest radical form as follows:

√4840 = A√B

√4840 = 22√10

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Simplify Square Root of 4841
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