Which two square roots are used to estimate Start Root 8 End Root?
A. Square Root 2 and Square Root 3
B. Square Root 3 and Square Root 4***
C. Square Root 4 and Square Root 9
D. Square Root 9 and Square Root 16
2021 Connexus 8th grade Estimating Irrationals Practice Correct answers are
c
b
d
b
These answers may be different for you but this is what is correct for me
the answers for the quick check "Estimating Irrationals"
are
1.c
2.b
3.c
4.c
5.c
It's C
no, 8 is between 4 and 9, right?
Well, well, well, let's do some estimating, shall we? If we're looking to estimate the square root of 8, we should choose the square roots that are closest to it. Option A, Square Root 2 and Square Root 3, are not quite there. Option B, Square Root 3 and Square Root 4, are inching closer, but nope, still not quite. Option C, Square Root 4 and Square Root 9, now we're getting warmer, but not quite. Ah, option D, Square Root 9 and Square Root 16. Bingo! Square Root 9 is 3, and Square Root 16 is 4, so those are the closest values to our estimated square root of 8.
To estimate the square root of 8, we can look for two perfect square roots that are closest to 8. In this case, we want to find two numbers a and b such that a² ≤ 8 ≤ b², where a < b.
Let's look at the options:
A. Square Root 2 and Square Root 3: If we square both 2 and 3, we get 2² = 4 and 3² = 9. Since 8 is between 4 and 9, this option is a possibility.
B. Square Root 3 and Square Root 4: If we square both 3 and 4, we get 3² = 9 and 4² = 16. Since 8 is between 9 and 16, this option is also a possibility.
C. Square Root 4 and Square Root 9: If we square both 4 and 9, we get 4² = 16 and 9² = 81. Since 8 is between 16 and 81, this option is not a good choice.
D. Square Root 9 and Square Root 16: If we square both 9 and 16, we get 9² = 81 and 16² = 256. Since 8 is between 81 and 256, this option is not a good choice.
Based on the options, both A (Square Root 2 and Square Root 3) and B (Square Root 3 and Square Root 4) are valid choices for estimating the square root of 8. However, option B is a better choice because 8 is closer to 9 (which is what the Square Root 3 represents) than it is to 4 (which is what the Square Root 2 represents).
Therefore, the correct answer is B. Square Root 3 and Square Root 4.