Using a number line west whole number and rational number to the nearest half is 105 square root between
10 and 11.
On the number line, we can approximate the value of the square root of 105 to the nearest half by finding whole numbers and rational numbers on either side of it.
First, we know that 10² = 100 and 11² = 121, so the square root of 105 must be between these two numbers.
Next, we can find some rational numbers on either side of 105 by taking the square root of nearby perfect squares:
- The square root of 100 is 10, so the nearest half would be 10.5
- The square root of 121 is 11, so the nearest half would be 11.5
Therefore, we can say that the square root of 105 rounded to the nearest half is between 10.5 and 11.5 on the number line.
i think that answer is incorrect
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Using a number line, what whole number and rational number to the nearest half is 10−−√ between?(1 point)
10−−√ is between
and
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Why did the square root go to the nearest half on the number line? Because it wanted to make sure it was well-rounded! So, let's locate it together. If we're looking for the square root of 105, we can start by finding the two perfect squares it falls between. The perfect squares closest to 105 are 100 (10 squared) and 121 (11 squared). So, the square root of 105 is somewhere between 10 and 11 on the number line. But let's not be irrational about it! Let's estimate it to the nearest half. Since 10.5 squared is 110.25, and 10 squared is 100, we know that the square root of 105 must be closer to 10 than to 10.5. Therefore, the answer to your question is approximately 10!
To find the nearest half to the square root of 105, we need to understand the concept of a number line and rational numbers.
A number line is a horizontal line that represents numbers. It is divided into segments or intervals by equally spaced marks. It extends infinitely in both directions, with zero at the center.
Whole numbers are integers that are greater than or equal to zero, such as 0, 1, 2, 3, etc.
Rational numbers are numbers that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero. Rational numbers can be positive or negative.
Now, let's find the square root of 105 using a number line:
1. Start by approximating the square root of 105. We know that 10 squared (10^2) is 100, and 11 squared (11^2) is 121. Therefore, the square root of 105 lies between 10 and 11.
2. Divide the interval between 10 and 11 into smaller parts. In this case, we divide it into halves since we want to find the nearest half.
10 10.5 11
3. To determine which half is closer to the square root of 105, we calculate the square of each value:
10^2 = 100
10.5^2 ≈ 110.25 (approximately)
11^2 = 121
As you can see, 10.5^2 is closer to 105 than 11^2. Therefore, the nearest half to the square root of 105 is 10.5.
In summary, using a number line and rational numbers, we found that the nearest half to the square root of 105 is 10.5.