Simplify Square Root of 62235

Here we will show you two methods that you can use to simplify the square root of 62235. In other words, we will show you how to find the square root of 62235 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.

√62235 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 62235 to simplify the square root of 62235. 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 62235. The factors of 62235 are 1, 3, 5, 9, 15, 27, 45, 135, 461, 1383, 2305, 4149, 6915, 12447, 20745, and 62235. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 62235 divided by the greatest perfect square from the list of all factors of 62235. We determined above that the greatest perfect square from the list of all factors of 62235 is 9. Furthermore, 62235 divided by 9 is 6915, therefore B equals 6915.

Now we have A and B and can get our answer to 62235 in its simplest radical form as follows:

√62235 = A√B

√62235 = 3√6915

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 62235 to simplify the square root of 62235 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 62235 and then take the square root of that product. The prime factors that multiply together to make 62235 are 3 x 3 x 3 x 5 x 461. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 62235 by the number (A) squared. 3 squared is 9 and 62235 divided by 9 is 6915. Therefore, B equals 6915.

Once again we have A and B and can get our answer to 62235 in its simplest radical form as follows:

√62235 = A√B

√62235 = 3√6915

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Simplify Square Root of 62236
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