The largest integer whose square root is an irrational number between 3 and 4 is 9.
To solve this, we need to find the largest perfect square that is less than or equal to 4. The largest perfect square less than or equal to 4 is 1 (1*1 = 1). Therefore, the square root of 1 is 1, which is not between 3 and 4.
The next largest perfect square is 4 (2*2 = 4). Therefore, the square root of 4 is 2, which is also not between 3 and 4.
The next largest perfect square is 9 (3*3 = 9). Therefore, the square root of 9 is 3, which is between 3 and 4.
Since there are no perfect squares between 4 and 9, the largest integer whose square root is an irrational number between 3 and 4 is 9.
Numbers Between Rational Numbers Practice
Math 8 Q1 (Pre-Algebra) / The Number System
What is the largest integer whose square root is an irrational number between 3 and 4?(1 point)
5 answers
no
Apologies for the mistake. Let's try again.
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 4.
The largest perfect square less than 4 is 1 (1 * 1 = 1), but the square root of 1 is 1, which is not between 3 and 4.
The next largest perfect square is 4 (2 * 2 = 4), but the square root of 4 is 2, which is not between 3 and 4.
The next largest perfect square is 9 (3 * 3 = 9). The square root of 9 is 3, which is between 3 and 4.
Therefore, the largest integer whose square root 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 4.
The largest perfect square less than 4 is 1 (1 * 1 = 1), but the square root of 1 is 1, which is not between 3 and 4.
The next largest perfect square is 4 (2 * 2 = 4), but the square root of 4 is 2, which is not between 3 and 4.
The next largest perfect square is 9 (3 * 3 = 9). The square root of 9 is 3, which is between 3 and 4.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 3.
Numbers Between Rational Numbers Practice
Math 8 Q1 (Pre-Algebra) / The Number System
Find a rational number with one decimal place that is between 17−−√
and 18−−√
.(1 point)
Math 8 Q1 (Pre-Algebra) / The Number System
Find a rational number with one decimal place that is between 17−−√
and 18−−√
.(1 point)
To find a rational number with one decimal place between √17 and √18, we can use the concept of average.
The average of two numbers is always a number between them. So we can find the average of √17 and √18 to get a rational number between them.
√17 ≈ 4.123
√18 ≈ 4.243
To find the average, add the two numbers and divide by 2:
(4.123 + 4.243) / 2 ≈ 4.183
Therefore, a rational number with one decimal place between √17 and √18 is approximately 4.2.
The average of two numbers is always a number between them. So we can find the average of √17 and √18 to get a rational number between them.
√17 ≈ 4.123
√18 ≈ 4.243
To find the average, add the two numbers and divide by 2:
(4.123 + 4.243) / 2 ≈ 4.183
Therefore, a rational number with one decimal place between √17 and √18 is approximately 4.2.