Question

the value of \\(\sqrt{17}\\) is between which two values on the number line?\
\\(\bigcirc\\) a. 1 and 2\
\\(\bigcirc\\) b. 3 and 4\
\\(\bigcirc\\) c. 16 and 17\
\\(\bigcirc\\) d. 4 and 5

Explanation:

Step1: Find nearest perfect squares

Identify perfect squares around 17: $4^2=16$ and $5^2=25$

Step2: Compare square roots

Take square roots of all terms: $\sqrt{16} < \sqrt{17} < \sqrt{25}$

Step3: Simplify the inequality

Simplify to get: $4 < \sqrt{17} < 5$

Answer:

D. 4 and 5