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)
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.
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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.
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)
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.
To find the largest integer whose square root is an irrational number between 3 and 4, we need to look for a perfect square that is just less than 4.
The perfect squares we can consider are 1, 4, 9, 16, 25, 36, 49, and so on.
The largest perfect square that is less than 4 is 1. The square root of 1 is 1, which is not between 3 and 4.
The next perfect square is 4. The square root of 4 is 2, which is also not between 3 and 4.
Moving on to the next perfect square, 9. The square root of 9 is 3, which falls between 3 and 4.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 9.
To find the largest integer whose square root is an irrational number between 3 and 4, we need to consider integers in that range and calculate their square roots.
Let's start by finding the square root of 3. Square root of 3 is an irrational number between 3 and 4, so we can continue testing the square roots of larger integers until we find the largest one.
Let's check the square root of 4: √4 = 2, which is not between 3 and 4, so we move on.
Next, let's check the square root of 5: √5 = 2.236, which is between 3 and 4.
Now, we move on to the square roots of larger integers.
Let's check the square root of 6: √6 = 2.449, which is between 3 and 4.
Next, let's check the square root of 7: √7 = 2.646, which is between 3 and 4.
Lastly, let's check the square root of 8: √8 = 2.828, which is not between 3 and 4.
Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 7, since the square root of 7 is approximately 2.646. So, the answer is 7.