Final answer:
To find the largest integer value of n for which 3√n is less than √200, simplify the expressions and solve the inequality. The largest integer value of n is 21.
Step-by-step explanation:
To determine the largest integer value of n for which 3√n is less than √200, we need to compare the two expressions and find a value of n that satisfies the inequality.
First, we simplify the expressions: 3√n and √200.
Since we want to find the largest integer value of n, we should take the largest possible value for √200, which is 14. So, we have: 3√n < 14.
Now, let's solve the inequality: √n < 14/3.
Squaring both sides of the inequality, we get: n < 196/9.
The largest integer value of n less than 196/9 is 21.