between which two tenths does \\(\\sqrt{3}\\) lie?\na. between 1.2 and 1.3\nb. between 1.4 and 1.5\nc…

Explanation:

Step1: Calculate squares of given tenths

First, we calculate the square of (1.7) and (1.8), (1.6) and (1.7), (1.4) and (1.5), (1.2) and (1.3).

• ((1.2)^2 = 1.44)
• ((1.3)^2 = 1.69)
• ((1.4)^2 = 1.96)
• ((1.5)^2 = 2.25)
• ((1.6)^2 = 2.56)
• ((1.7)^2 = 2.89)
• ((1.8)^2 = 3.24)

Step2: Compare with (3)

We know that (\sqrt{3}) is the number whose square is (3). So we check between which two squares (3) lies. We see that (2.89< 3< 3.24), which means ((1.7)^2< 3<(1.8)^2). Taking square roots (since square root is a monotonically increasing function for non - negative numbers), we get (1.7 < \sqrt{3}< 1.8).

Answer:

D. Between 1.7 and 1.8