Question

show your work using the number line.
estimate the value of $sqrt{8}$

Explanation:

Step1: Identify nearby perfect squares

$2^2=4$, $3^2=9$

Step2: Locate $\sqrt{8}$ between integers

Since $4<8<9$, $\sqrt{4}<\sqrt{8}<\sqrt{9}$, so $2<\sqrt{8}<3$

Step3: Narrow the estimate

Calculate midpoint value: $2.5^2=6.25$. Since $6.25<8$, $\sqrt{8}$ is between 2.5 and 3.
Calculate $2.8^2=7.84$, $2.9^2=8.41$. Since $7.84<8<8.41$, $\sqrt{8}$ is between 2.8 and 2.9, closer to 2.8.

Step4: Plot on number line

Mark 2 and 3 on the number line. Divide the segment between 2 and 3 into 10 equal parts. Plot $\sqrt{8}$ ~2.8, 8 tenths from 2 towards 3.

Answer:

The estimated value of $\sqrt{8}$ is approximately 2.8, located between 2 and 3 on the number line, closer to 3, 0.8 units from 2.