Simplify Square Root of 77910

Here we will show you two methods that you can use to simplify the square root of 77910. In other words, we will show you how to find the square root of 77910 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.

√77910 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77910 to simplify the square root of 77910. 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 77910. The factors of 77910 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 53, 70, 98, 105, 106, 147, 159, 210, 245, 265, 294, 318, 371, 490, 530, 735, 742, 795, 1113, 1470, 1590, 1855, 2226, 2597, 3710, 5194, 5565, 7791, 11130, 12985, 15582, 25970, 38955, and 77910. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 77910 divided by the greatest perfect square from the list of all factors of 77910. We determined above that the greatest perfect square from the list of all factors of 77910 is 49. Furthermore, 77910 divided by 49 is 1590, therefore B equals 1590.

Now we have A and B and can get our answer to 77910 in its simplest radical form as follows:

√77910 = A√B

√77910 = 7√1590

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77910 to simplify the square root of 77910 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 77910 and then take the square root of that product. The prime factors that multiply together to make 77910 are 2 x 3 x 5 x 7 x 7 x 53. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 77910 by the number (A) squared. 7 squared is 49 and 77910 divided by 49 is 1590. Therefore, B equals 1590.

Once again we have A and B and can get our answer to 77910 in its simplest radical form as follows:

√77910 = A√B

√77910 = 7√1590

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