Question

which is the best estimate for \\(\sqrt{45}\\)? 7.5 5.2 6.3 6.7

Explanation:

Step1: Recall square values

We know that $6^2 = 36$ and $7^2 = 49$. Since $45$ is between $36$ and $49$, $\sqrt{45}$ is between $6$ and $7$.

Step2: Calculate closer value

Calculate $6.7^2 = 6.7\times6.7 = 44.89$, which is very close to $45$.
Calculate $6.3^2 = 6.3\times6.3 = 39.69$, $5.2^2 = 27.04$, $7.5^2 = 56.25$.
Among the options, $6.7^2 = 44.89$ is closest to $45$, so $\sqrt{45}\approx6.7$.

Answer:

6.7 (the option with 6.7, as its square is closest to 45)