Final answer:
To approximate the square root of 34 to the nearest integer, you can find the perfect square that is closest to 34. The square root of that perfect square will be an approximation of the square root of 34.
Step-by-step explanation:
Perfect Squares and Estimation
Identify the perfect squares closest to 34:
The nearest perfect square less than 34 is 25.
The nearest perfect square greater than 34 is 36.
Estimate the square root:
Since 34 is closer to 25 than 36, we know the square root of 34 is closer to 5 than 6.
Choose the nearest integer:
Since 5.83 is closer to 5 than 6, the nearest integer approximation for the square root of 34 is 5.
Therefore, both methods lead to the same answer: the square root of 34 approximated to the nearest integer is 5.