What Is the Square Root of 72?

The square root of 72 is approximately 8.49 when rounded to the nearest hundredth. Since it is not a perfect square, it can most easily be solved by using a scientific calculator. If this option is unavailable, there are a few tricks you can do to arrive at a solution.

To figure this problem without a calculator, first identify the two nearest perfect squares that surround the number 72. A perfect square is a number that can be divided by a whole number and yield the same whole number. For instance, 25 divided by 5 equals 5. So the square root of 25 is 5. Other perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 36 (6 x 6) and 49 (7 x 7).

In the case of 72, the numbers are 8 and 9. Multiplying 8 by 8 gives you 64, and multiplying 9 by 9 results in 81. 72 falls in between. Next, divide 72 by either 8 or 9. For instance, 72÷8=9. Now, determine the average of that result and the original square you used (8 or 9) like so: (9+8)/2=8.5. Finally, continue repeating the previous two steps until you arrive at the desired accuracy.