Simplify Square Root of 70400

Here we will show you two methods that you can use to simplify the square root of 70400. In other words, we will show you how to find the square root of 70400 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.

√70400 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 70400 to simplify the square root of 70400. 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 70400. The factors of 70400 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 64, 80, 88, 100, 110, 128, 160, 176, 200, 220, 256, 275, 320, 352, 400, 440, 550, 640, 704, 800, 880, 1100, 1280, 1408, 1600, 1760, 2200, 2816, 3200, 3520, 4400, 6400, 7040, 8800, 14080, 17600, 35200, and 70400. Furthermore, the greatest perfect square on this list is 6400 and the square root of 6400 is 80. Therefore, A equals 80.

B = Calculate 70400 divided by the greatest perfect square from the list of all factors of 70400. We determined above that the greatest perfect square from the list of all factors of 70400 is 6400. Furthermore, 70400 divided by 6400 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 70400 in its simplest radical form as follows:

√70400 = A√B

√70400 = 80√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 70400 to simplify the square root of 70400 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 70400 and then take the square root of that product. The prime factors that multiply together to make 70400 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 = 6400 and the square root of 6400 is 80. Therefore, A equals 80.

B = Divide 70400 by the number (A) squared. 80 squared is 6400 and 70400 divided by 6400 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 70400 in its simplest radical form as follows:

√70400 = A√B

√70400 = 80√11

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Simplify Square Root of 70401
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