The square root of 68 is approximately 8.2462. To find the square root of a number, you want to determine what number, when multiplied by itself, equals the original number. In this case, since 68 is not a perfect square, we can simplify it by breaking it down into its prime factors.
68 can be factored into 4 and 17. The square root of 4 is 2, so we can express the square root of 68 as:
- √68 = √(4 × 17)
- √68 = √4 × √17
- √68 = 2√17
Using a calculator, we can find that the approximate value of √17 is about 4.1231. Therefore, when you multiply 2 by this value, you get:
2 × 4.1231 ≈ 8.2462
So, the square root of 68 simplifies to 2 times the square root of 17, leading us to an approximate value of 8.2462.