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
The sign of the product of two numbers is determined by the signs of the numbers being multiplied. In this case, we are multiplying 1732 by -110.
Since one of the numbers is negative, the product will be negative.
Therefore, the sign of the product of 1732 and -110 is $\boxed{\text{negative}}$.
is the answer negative?
No, the answer is not negative. The product of 1732 and -110 is positive.
Determine the sign of the product of −0.708×−6.24.(1 point)
Responses
A. both positive and negative
both positive and negative
B. The product has no sign.
The product has no sign.
C. negative
negative
D. positive
The product of two negative numbers is always positive.
Therefore, the sign of the product of -0.708 and -6.24 is $\boxed{\text{positive}}$.