Using a number line, what is the approximate value of 19−−√?
A:4.38
B:4.13
C:4.5
D:4.25
We can estimate the value of $\sqrt{19}$ by finding the two perfect squares that $\sqrt{19}$ is between. The perfect squares closest to 19 are 16 and 25. Since 19 is closer to 16 than it is to 25, we can estimate $\sqrt{19}$ to be a little greater than $\sqrt{16}=4$. Therefore, the approximate value of $19-\sqrt{19}$ can be estimated to be a little less than $19-4=15$. However, we can get a more accurate estimate by noting that $\sqrt{19} \approx 4.36$, since $4.36^2=18.9696$. Therefore, $19-\sqrt{19} \approx 19-4.36 = \boxed{14.64}$, which is closest to answer choice $\boxed{\textbf{(D) }4.25}$.
Using a number line, what whole number and rational number to the nearest half is 105−√ between?
A:between 9.5 and 10
B:between 11 and 11.5
C:between 10 and 10.5
D:between 10.5 and 11
We can estimate the value of $\sqrt{105}$ by finding the two perfect squares that $\sqrt{105}$ is between. The perfect squares closest to 105 are 100 and 121. Since 105 is closer to 100 than it is to 121, we can estimate $\sqrt{105}$ to be a little greater than $\sqrt{100}=10$. Therefore, the approximate value of $105-\sqrt{105}$ can be estimated to be a little less than $105-10=95$. However, we can get a more accurate estimate by noting that $\sqrt{105} \approx 10.25$, since $10.25^2=105.0625$. Therefore, $105-\sqrt{105} \approx 105-10.25 = 94.75$. To the nearest half, this is between $\boxed{\textbf{(B) }11 \text{ and } 11.5}.$
Determine the sign of the product of −152×−1. Enter + for positive or – for negative.
To determine the sign of the product $-152 \times -1$, we can consider the rule that states: the product of two negative numbers is positive.
Since $-152$ and $-1$ are both negative, their product will be positive.
Therefore, the sign of the product $-152 \times -1$ is $\boxed{+}$ (positive).
Multiply 7×−4.
When multiplying a positive number by a negative number, the result is always negative.
Therefore, $7 \times -4 = \boxed{-28}$.
−28×−19
When multiplying two negative numbers, the result is always positive.
Therefore, $-28 \times -19 = \boxed{532}$.
Determine the sign of the product of 1732×(−110).(1 point)
Responses
negative
negative
The product has no sign.
The product has no sign.
positive
positive
both positive and negative