Question

let a, b, c, d, e, f, and g be positive numbers.
given these equations, arrange a, b, c, d, e, f, and g from least to greatest. explain your reasoning.
a. $a^2 = 6$
b. $b^3 = 7$
c. $c^2 = 8$
d. $d^2 = 7$
e. $e^3 = 8$
f. $f^2 = 9$
g. $g^3 = 11$
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Explanation:

Step1: Solve for each variable

$a = \sqrt{6} \approx 2.449$, $b = \sqrt[3]{7} \approx 1.913$, $c = \sqrt{8} \approx 2.828$, $d = \sqrt{7} \approx 2.646$, $e = \sqrt[3]{8} = 2$, $f = \sqrt{9} = 3$, $g = \sqrt[3]{11} \approx 2.224$

Step2: Compare approximate values

Order the decimals from smallest to largest: $1.913 < 2 < 2.224 < 2.449 < 2.646 < 2.828 < 3$

Step3: Map to original variables

Match each decimal to its corresponding variable.

Answer:

$b < e < g < a < d < c < f$