Simplify Square Root of 24400

Here we will show you two methods that you can use to simplify the square root of 24400. In other words, we will show you how to find the square root of 24400 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.

√24400 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24400 to simplify the square root of 24400. 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 24400. The factors of 24400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 61, 80, 100, 122, 200, 244, 305, 400, 488, 610, 976, 1220, 1525, 2440, 3050, 4880, 6100, 12200, and 24400. Furthermore, the greatest perfect square on this list is 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Calculate 24400 divided by the greatest perfect square from the list of all factors of 24400. We determined above that the greatest perfect square from the list of all factors of 24400 is 400. Furthermore, 24400 divided by 400 is 61, therefore B equals 61.

Now we have A and B and can get our answer to 24400 in its simplest radical form as follows:

√24400 = A√B

√24400 = 20√61

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24400 to simplify the square root of 24400 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 24400 and then take the square root of that product. The prime factors that multiply together to make 24400 are 2 x 2 x 2 x 2 x 5 x 5 x 61. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 5 x 5 = 400 and the square root of 400 is 20. Therefore, A equals 20.

B = Divide 24400 by the number (A) squared. 20 squared is 400 and 24400 divided by 400 is 61. Therefore, B equals 61.

Once again we have A and B and can get our answer to 24400 in its simplest radical form as follows:

√24400 = A√B

√24400 = 20√61

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Simplify Square Root of 24401
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