Practice - Algebra 1

9.5.5 Practice

9.5.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

Solve each equation and write the solutions using the ± notation, then choose the correct solution from the list.

$x^2=144$

$x= \pm\; 24$
$x= \pm\; 12$
$x= \pm\; 72$
$x= \pm\; 144$

$x^2=5$

$x= \pm\; \sqrt{10}$
$x= \pm\; \frac{5}{2}$
$x= \pm\; 5$
$x= \pm\; \sqrt{5}$

$4x^2=28$

$x= \pm\; \sqrt{7}$
$x= \pm\; \frac{7}{2}$
$x= \pm\; 7$
$x= \pm\; \sqrt {\frac{7}{2}}$

$x^2=\frac{25}{4}$

$x= \pm\; \frac{5}{4}$
$x= \pm\; \frac{10}{2}$
$x= \pm\; \frac{5}{2}$
$x= \pm\; \frac{25}{4}$

$2x^2=22$

$x= \pm\; \sqrt{11}$
$x= \pm\; \frac{11}{2}$
$x= \pm\; 11$
$x= \pm\; \sqrt{\frac{11}{2}}$

$7x^2=16$

$x= \pm\; \frac {\sqrt{16}}{7}$
$x= \pm\; 8$
$x= \pm\; 16$
$x= \pm\; \sqrt{\frac{16}{7}}$

For each expression, choose an equivalent expression.

$10 \pm \sqrt{4}$

$4+ \sqrt{10}$ and $4- \sqrt{10}$
3 and 5
8 and 12
$4+ \sqrt{2}$ and $4- \sqrt{2}$
$-17$ and $5$

$4 \pm \sqrt{10}$

$4+ \sqrt{10}$ and $4- \sqrt{10}$
3 and 5
8 and 12
$4+ \sqrt{2}$ and $4- \sqrt{2}$
$-17$ and $5$

$\sqrt{16} \pm \sqrt{2}$

$4+ \sqrt{10}$ and $4- \sqrt{10}$
3 and 5
8 and 12
$4+ \sqrt{2}$ and $4- \sqrt{2}$
$-17$ and $5$

What is the difference between $\sqrt{9}$ and the solutions to $x^2=9$ ?

There is no difference; they are equal.
$\sqrt{9}$ is equal to 3, while there are two numbers that make $x^2=9$ true: 3 and -3.
$\sqrt{9}$ is equal to -3, while there are two numbers that make $x^2=9$ true: 3 and -3.
$\sqrt{9}$ is equal to 3, while $x^2=9$ is equal to -3.

Technology required. For each equation, find the exact solutions by completing the square and the approximate solutions by graphing. Then, verify that the solutions found using the two methods are close.

Solve the equation $x^2+10x+8=0$ by completing the square. Select two exact solutions.

$x= -5+ \sqrt{17}$
$x=5+ \sqrt{17}$
$x=5- \sqrt{17}$
$x= -5- \sqrt{17}$

Choose the graph that best represents the equation $x^2+10x+8=0$ .

Graph A	Graph B
Graph C	Graph D

A
B
C
D

Are the solutions and the graph for the equation $x^2+10x+8=0$ similar?

They are similar because the square root of a number is always positive.
They are not similar because the square root of a number is always positive.
They are similar because the solutions are close.
They are not similar.

Answer the following questions about $x^2-4x-11=0$ .

Solve the equation $x^2-4x-11=0$ by completing the square. Select two exact solutions.

$x=-2+ \sqrt{15}$
$x=2+ \sqrt{15}$
$x=2- \sqrt{15}$
$x=-2- \sqrt{15}$

Choose the graph that best represents the equation $x^2-4x-11=0$ .

Graph A	Graph B
Graph C	Graph D

A
B
C
D

Are the solutions and the graph for the equation $x^2-4x-11=0$ similar?

They are similar because the square root of a number is always positive.
They are not similar.
They are not similar because the square root of a number is always positive.
They are similar because the solutions are close