Question

enhanced algebra: concepts and connections – unit 3 georgia’s k-12 mathematics standards name: _____________ date: ______ formative assessment solve and explain the reasoning behind the solutions. hint: some may have multiple solutions. a. $a^2 = 6$ b. $b^3 = 7$ c. $c^3 = 8$ d. $d^2 = 7$ e. $e^3 = -8$ f. $f^2 = 9$ g. $g^3 = 11$

Explanation:

Step1: Solve quadratic $a^2=6$

Take square roots: $a=\pm\sqrt{6}$

Step2: Solve cubic $b^3=7$

Take cube root: $b=\sqrt[3]{7}$

Step3: Solve cubic $c^3=8$

$2^3=8$, so $c=2$

Step4: Solve quadratic $d^2=7$

Take square roots: $d=\pm\sqrt{7}$

Step5: Solve quadratic $e^2=-8$

No real square root of negative: No real solutions

Step6: Solve quadratic $f^2=9$

$\pm3^2=9$, so $f=\pm3$

Step7: Solve cubic $g^3=11$

Take cube root: $g=\sqrt[3]{11}$

Answer:

A. $a = \sqrt{6}, a = -\sqrt{6}$
B. $b = \sqrt[3]{7}$
C. $c = 2$
D. $d = \sqrt{7}, d = -\sqrt{7}$
E. No real solutions
F. $f = 3, f = -3$
G. $g = \sqrt[3]{11}$