Rational numbers
What is the largest integer square root is an irrational number between 3 and 4?
The largest integer square root that is an irrational number between 3 and 4 is 3.
To find the largest integer whose square root is an irrational number between 3 and 4, we need to find the largest perfect square that is less than 16 (the square of 4) but greater than 9 (the square of 3).
Starting with 3, we can calculate its square: 3^2 = 9.
Next, we calculate the square of 4: 4^2 = 16.
Since the largest perfect square less than 16 and greater than 9 is 9, whose square root is 3, the largest integer whose square root is an irrational number between 3 and 4 is 3.
To determine the largest integer whose square root is an irrational number between 3 and 4, we need to find two consecutive perfect squares that sandwich an irrational number.
First, let's find the perfect square slightly smaller than 3:
The square root of 3 is approximately 1.732, so the closest perfect square below 3 is 1^2 = 1.
Next, let's find the perfect square slightly larger than 4:
The square root of 4 is 2.
Hence, we have found that the perfect squares 1 and 4 sandwich an irrational number between 3 and 4. Since 1 is the largest integer whose square root is irrational in this range, the answer is 1.