Question

exam study guide december 2 2. evaluate \\(\sqrt3{216}\\) *know how to find cube roots using calculators! 4. express the fraction \\(\frac{7}{9}\\) as a decimal. round to the nearest hundredth.

Explanation:

Problem 2: Evaluate $\boldsymbol{\sqrt[3]{216}}$

Step1: Recall cube root definition

A cube root of a number $x$ is a number $y$ such that $y^3 = x$. We need to find $y$ where $y^3 = 216$.

Step2: Find the cube root

We know that $6^3 = 6\times6\times6 = 216$. So, $\sqrt[3]{216}=6$.

Problem 4: Express $\boldsymbol{\frac{7}{9}}$ as a decimal (round to nearest hundredth)

Step1: Perform division

Divide 7 by 9: $7\div9 = 0.777\ldots$ (this is a repeating decimal).

Step2: Round to hundredth

The hundredth place is the second decimal digit. The third decimal digit is 7, which is $\geq5$, so we round up the second decimal digit. Thus, $0.777\ldots\approx0.78$.

Final Answers:

Problem 2: $\boldsymbol{6}$
Problem 4: $\boldsymbol{0.78}$

Answer:

Step1: Perform division

Divide 7 by 9: $7\div9 = 0.777\ldots$ (this is a repeating decimal).

Step2: Round to hundredth

The hundredth place is the second decimal digit. The third decimal digit is 7, which is $\geq5$, so we round up the second decimal digit. Thus, $0.777\ldots\approx0.78$.

Final Answers:

Problem 2: $\boldsymbol{6}$
Problem 4: $\boldsymbol{0.78}$