Simplify Square Root of 85851

Here we will show you two methods that you can use to simplify the square root of 85851. In other words, we will show you how to find the square root of 85851 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.

√85851 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85851 to simplify the square root of 85851. 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 85851. The factors of 85851 are 1, 3, 9, 9539, 28617, and 85851. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 85851 divided by the greatest perfect square from the list of all factors of 85851. We determined above that the greatest perfect square from the list of all factors of 85851 is 9. Furthermore, 85851 divided by 9 is 9539, therefore B equals 9539.

Now we have A and B and can get our answer to 85851 in its simplest radical form as follows:

√85851 = A√B

√85851 = 3√9539

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85851 to simplify the square root of 85851 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 85851 and then take the square root of that product. The prime factors that multiply together to make 85851 are 3 x 3 x 9539. 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 85851 by the number (A) squared. 3 squared is 9 and 85851 divided by 9 is 9539. Therefore, B equals 9539.

Once again we have A and B and can get our answer to 85851 in its simplest radical form as follows:

√85851 = A√B

√85851 = 3√9539

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Simplify Square Root of 85852
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