Question

fill in each circle with >, < or = to make a true statement.

1. $-\frac{5}{6}\bigcirc-sqrt{2}$
2. $sqrt{14}\bigcirc4$

find the approximate value of each expression and plot both values on the provided number line.

1. $2sqrt{8}$
2. $pi - 6$

Explanation:

Step1: Compare $-\frac{5}{6}$ and $-\sqrt{2}$

Find decimal - values. $-\frac{5}{6}\approx - 0.83$, $-\sqrt{2}\approx - 1.41$. Since $-0.83>-1.41$, so $-\frac{5}{6}>-\sqrt{2}$.

Step2: Compare $\sqrt{14}$ and $4$

Square both sides. $(\sqrt{14})^2 = 14$, $4^2=16$. Since $14 < 16$, so $\sqrt{14}<4$.

Step3: Approximate $2\sqrt{8}$

Simplify $\sqrt{8}=2\sqrt{2}$, then $2\sqrt{8}=2\times2\sqrt{2}=4\sqrt{2}$. $\sqrt{2}\approx1.414$, so $2\sqrt{8}=4\sqrt{2}\approx4\times1.414 = 5.656\approx5.66$.

Step4: Approximate $\pi - 6$

We know that $\pi\approx3.14$, so $\pi - 6\approx3.14 - 6=-2.86$.

Answer:

1. $-\frac{5}{6}>-\sqrt{2}$
2. $\sqrt{14}<4$
3. $2\sqrt{8}\approx 5.66$
4. $\pi - 6\approx - 2.86$