Question

Using the fact that 1.4 < √2 < 1.5 and 1.7 < √3 < 1.8, find the possible values of √3-√2

A) 0.1
B) 0.2
C) 0.3
D) 0.4

Answer 1

By utilizing the provided inequalities for square roots of 2 and 3, the possible values for √3 - √2 are between 0.2 and 0.4, which excludes option A) 0.1 and includes options B) 0.2, C) 0.3, and D) 0.4.

Step-by-step explanation:

Mathematics

often involves working with inequalities to find possible values of expressions. Using the given inequalities,

1.4 < √2 < 1.5

and

1.7 < √3 < 1.8

, we can estimate the value of

√3 - √2

. The largest possible value occurs when √3 is at its maximum (1.8) and √2 is at its minimum (1.4), which would be 1.8 - 1.4 = 0.4. Conversely, the smallest possible value for √3 - √2 occurs when √3 is at its minimum (1.7) and √2 is at its maximum (1.5), yielding a difference of 1.7 - 1.5 = 0.2. Thus, the possible values for √3 - √2 fall between 0.2 and 0.4.