Simplify Square Root of 78484

Here we will show you two methods that you can use to simplify the square root of 78484. In other words, we will show you how to find the square root of 78484 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.

√78484 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78484 to simplify the square root of 78484. 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 78484. The factors of 78484 are 1, 2, 4, 7, 14, 28, 2803, 5606, 11212, 19621, 39242, and 78484. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 78484 divided by the greatest perfect square from the list of all factors of 78484. We determined above that the greatest perfect square from the list of all factors of 78484 is 4. Furthermore, 78484 divided by 4 is 19621, therefore B equals 19621.

Now we have A and B and can get our answer to 78484 in its simplest radical form as follows:

√78484 = A√B

√78484 = 2√19621

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78484 to simplify the square root of 78484 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 78484 and then take the square root of that product. The prime factors that multiply together to make 78484 are 2 x 2 x 7 x 2803. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 78484 by the number (A) squared. 2 squared is 4 and 78484 divided by 4 is 19621. Therefore, B equals 19621.

Once again we have A and B and can get our answer to 78484 in its simplest radical form as follows:

√78484 = A√B

√78484 = 2√19621

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Simplify Square Root of 78485
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