Question

1. point q is shown on the number line. which value is best represented by point q? a $sqrt{5.4}$ b $sqrt{29.5}$ c $sqrt{35.5}$

Explanation:

Step1: Identify Q's range

Point Q is between 5 and 6, so $5 < Q < 6$. Square all values: $5^2=25$, $6^2=36$, so $25 < Q^2 < 36$.

Step2: Evaluate option A

Calculate $(\sqrt{5.4})^2 = 5.4$. $5.4 < 25$, so it is too small.

Step3: Evaluate option B

Calculate $(\sqrt{29.5})^2 = 29.5$. $25 < 29.5 < 36$, so it fits the range.

Step4: Evaluate option C

Calculate $(\sqrt{35.5})^2 = 35.5$. $35.5$ is very close to 36, meaning $\sqrt{35.5} \approx 5.96$, which would be near 6, not the position of Q (closer to the middle of 5 and 6).

Answer:

B. $\sqrt{29.5}$