which two square roots are used to estimate √8
A. √4 and √9
B√9 and √19
To estimate the square root of 8, we need to find two square roots that are closest to 8.
A. √4 is 2 and √9 is 3. These numbers are not close to 8, so this option is not correct.
B. √9 is 3. This is the closest square root to 8. However, √19 is not a square root that is close to 8.
Therefore, neither option A nor option B has two square roots that are used to estimate √8 accurately.
To estimate √8, we need to find two square roots that surround the number 8.
Options A and B are as follows:
A. √4 and √9
B. √9 and √19
Let's evaluate each option to find out which one is accurate.
Option A: √4 and √9
√4 is equal to 2, and √9 is equal to 3.
These two square roots do not surround the number 8.
Option B: √9 and √19
√9 is equal to 3, and √19 is a decimal value around 4.
These two square roots surround the number 8.
Therefore, option B, √9 and √19, is the correct answer for estimating √8.
To estimate √8, we need to find the two square roots that closely bound the actual value of √8.
Let's look at option A: √4 and √9.
√4 is equal to 2, and √9 is equal to 3.
Since √8 is greater than 2 (√4) and less than 3 (√9), using these values as estimates would give us an estimation range of 2 to 3.
Now, let's consider option B: √9 and √19.
√9 is still equal to 3, but √19 is greater than 3 (since 19 is greater than 9).
Using these values as estimates would give us a range going from 3 (lower bound) to greater than 3 (upper bound).
Therefore, option A (√4 and √9) is the correct choice for estimating √8, as it provides a smaller estimation range.