Question

1. find the perimeter of the triangle below. write your answer in simplest radical form. 3\sqrt4{80} 8\sqrt4{5} \sqrt3{24}

Explanation:

Step1: Simplify $\sqrt[4]{80}$

Factor 80 into $16 \times 5$, so $3\sqrt[4]{80} = 3\sqrt[4]{16 \times 5} = 3 \times 2\sqrt[4]{5} = 6\sqrt[4]{5}$

Step2: Simplify $\sqrt[3]{24}$

Factor 24 into $8 \times 3$, so $\sqrt[3]{24} = \sqrt[3]{8 \times 3} = 2\sqrt[3]{3}$

Step3: Combine like radicals

Add the fourth-root terms: $6\sqrt[4]{5} + 8\sqrt[4]{5} = 14\sqrt[4]{5}$

Step4: Sum all side lengths

Perimeter = $14\sqrt[4]{5} + 2\sqrt[3]{3}$

Answer:

$14\sqrt[4]{5} + 2\sqrt[3]{3}$