Simplify Square Root of 61852

Here we will show you two methods that you can use to simplify the square root of 61852. In other words, we will show you how to find the square root of 61852 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.

√61852 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 61852 to simplify the square root of 61852. 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 61852. The factors of 61852 are 1, 2, 4, 7, 14, 28, 47, 94, 188, 329, 658, 1316, 2209, 4418, 8836, 15463, 30926, and 61852. Furthermore, the greatest perfect square on this list is 8836 and the square root of 8836 is 94. Therefore, A equals 94.

B = Calculate 61852 divided by the greatest perfect square from the list of all factors of 61852. We determined above that the greatest perfect square from the list of all factors of 61852 is 8836. Furthermore, 61852 divided by 8836 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 61852 in its simplest radical form as follows:

√61852 = A√B

√61852 = 94√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 61852 to simplify the square root of 61852 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 61852 and then take the square root of that product. The prime factors that multiply together to make 61852 are 2 x 2 x 7 x 47 x 47. When we strip out the pairs only, we get 2 x 2 x 47 x 47 = 8836 and the square root of 8836 is 94. Therefore, A equals 94.

B = Divide 61852 by the number (A) squared. 94 squared is 8836 and 61852 divided by 8836 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 61852 in its simplest radical form as follows:

√61852 = A√B

√61852 = 94√7

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Simplify Square Root of 61853
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