which two square roots are used to estimate \sqrt(8) A. \sqrt(2) and \sqrt(3) B. \sqrt(3) and \sqrt(4) C. \sqrt(4) and \sqrt(9) D. \sqrt(9) and \sqrt(19)
A. √2 and √3
To estimate √8, we need to find two square roots that are close to the value of √8.
A. √2 and √3 - √2 = 1.41 and √3 = 1.73. Both of these square roots are less than √8.
B. √3 and √4 - √3 = 1.73 and √4 = 2. Both of these square roots are less than √8.
C. √4 and √9 - √4 = 2 and √9 = 3. Both of these square roots are greater than √8.
D. √9 and √19 - √9 = 3 and √19 ≈ 4.36. Both of these square roots are greater than √8.
Based on the options provided, the two closest square roots to estimate √8 are A. √2 and √3.
To estimate √8, we can use the square roots of numbers that are close to 8. Let's consider the given options:
A. √2 and √3: √2 ≈ 1.41, √3 ≈ 1.73
B. √3 and √4: √3 ≈ 1.73, √4 = 2
C. √4 and √9: √4 = 2, √9 = 3
D. √9 and √19: √9 = 3, √19 ≈ 4.36
From the options, we can see that option C (\(\sqrt{4}\) and \(\sqrt{9}\)) provides the square roots closest to 8, which are 2 and 3. Therefore, the correct answer is option C.