Question

unit 5 assessment: alg 2 25 pts name

1. simplify: $sqrt3{27x^{9}y^{3}}$ (3 pts)

1. $121\frac{1}{11}$ is equivalent to (1 pt)

□2 □ $sqrt11{121}$
□11 □ $sqrt{121^{11}}$

1. the graph of $y = \sqrt{x}$ has been translated to the right 3 units and down 9 units.

what is the equation of the translated graph? (1 pt)
a. $y = \sqrt{x+9}+3$ b. $y = \sqrt{x+3}-9$
c. $y = -\sqrt{9-x}+3$ d. $y = \sqrt{x-3}-9$

1. multiply and simplify (show work):

$(a+\sqrt{5})(a-\sqrt{5})$ (3 pts)

a. $a^{2}+\sqrt{25}$ c. $a^{2}+5$
b. $a^{2}-5$ d. $a^{2}-25$

1. which expression is equivalent to

$\left(\sqrt3{17}\
ight)^{4}$? (1 pt)
a. $17^{\frac{3}{4}}$ c. $17^{\frac{4}{3}}$
b. $17^{12}$ d. $\frac{4^{17}}{3}$

Explanation:

Step1: Factor radicand into cubes

$\sqrt[3]{27x^9y^3} = \sqrt[3]{3^3 \cdot (x^3)^3 \cdot y^3}$

Step2: Extract cube roots

$3 \cdot x^3 \cdot y$

Step1: Rewrite exponent as root form

$121^{\frac{1}{11}} = \sqrt[11]{121}$

Step1: Apply horizontal translation rule

For right shift 3: $\sqrt{x-3}$

Step2: Apply vertical translation rule

For down shift 9: $\sqrt{x-3} - 9$

Step1: Use difference of squares formula

$(a+b)(a-b)=a^2-b^2$, let $b=\sqrt{5}$

Step2: Compute the squared terms

$a^2 - (\sqrt{5})^2 = a^2 - 5$

Answer:

$3x^3y$

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