Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Aug 17, 2023

Find the range of whole numbers that contain $\sqrt{40}$ . $\sqrt{40}$ lies between $\lfloor\sqrt{40}\rfloor$ and $\lceil\sqrt{40}\rceil$ .

STEP 1

Assumptions1. We are asked to find two consecutive whole numbers between which $\sqrt{40}$ lies. . We know that $\sqrt{40}$ is a real number.

STEP 2

First, we need to find the square root of40.
$\sqrt{40}$

STEP 3

Calculate the square root of40.
$\sqrt{40} \approx6.32$

STEP 4

Now that we have the square root of40, we can see that it is greater than6 and less than7.
$6 < \sqrt{40} <7$

STEP 5

So, the two consecutive whole numbers between which $\sqrt{40}$ lies are and7.
The sentence to justify the answer is "The square root of40, which is approximately.32, lies between the two consecutive whole numbers and7."

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