Question

select the two correct answers.
which expressions have a value between $-3$ and $-2$?
$\square$ $1 + \pi$
$\square$ $-\frac{5\pi}{4}$
$\square$ $-\pi$
$\square$ $-2\sqrt{2.2}$
$\square$ $1 - \pi$
$\square$ $2 - \sqrt{2.2}$

Explanation:

Step1: Recall approximate value of $\pi$

$\pi \approx 3.1416$

Step2: Calculate value of $1+\pi$

$1+\pi \approx 1+3.1416=4.1416$

Step3: Calculate value of $-\frac{5\pi}{4}$

$-\frac{5\pi}{4} \approx -\frac{5\times3.1416}{4}=-3.927$

Step4: Calculate value of $-\pi$

$-\pi \approx -3.1416$

Step5: Calculate value of $-2\sqrt{2.2}$

First, $\sqrt{2.2}\approx1.483$, so $-2\sqrt{2.2}\approx-2\times1.483=-2.966$

Step6: Calculate value of $1-\pi$

$1-\pi \approx 1-3.1416=-2.1416$

Step7: Calculate value of $2-\sqrt{2.2}$

$2-\sqrt{2.2}\approx2-1.483=0.517$

Step8: Check values between -3 and -2

Values in $(-3,-2)$ are $-2.966$ and $-2.1416$.

Answer:

• $-2\sqrt{2.2}$
• $1-\pi$