What Is the Square Root of 72?

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.