Question

1. the $sqrt{40}$ is between which two numbers?

a 6 and 7
b 9 and 10
c 19 and 20
d 20 and 21

Explanation:

Step1: Find squares of nearby integers

Calculate squares of integers around the estimate of $\sqrt{40}$:
$6^2 = 36$, $7^2 = 49$

Step2: Compare with 40

Check where 40 falls relative to these squares:
$36 < 40 < 49$

Step3: Relate back to square roots

Take square roots of all parts of the inequality:
$\sqrt{36} < \sqrt{40} < \sqrt{49}$
$6 < \sqrt{40} < 7$

Answer:

A. 6 and 7