Problem

1. Exprime l'expression suivante, comportant des radicaux, sous sa forme simplifiée. $4 \sqrt{20}+\sqrt{24}-\sqrt{45}-3 \sqrt{54}$ 2. Simplifie l'expression suivante. \[ -5 \sqrt[3]{2}+\sqrt[3]{54}+5 \sqrt{2} \]

Solution

Step 1 :\(4 \sqrt{20}+\sqrt{24}-\sqrt{45}-3 \sqrt{54}\)

Step 2 :\(4 \sqrt{4 \cdot 5}+\sqrt{6 \cdot 4}-\sqrt{9 \cdot 5}-3 \sqrt{9 \cdot 6}\)

Step 3 :\(4 \cdot 2 \sqrt{5}+\sqrt{6} \cdot \sqrt{4}-\sqrt{9} \cdot \sqrt{5}-3 \cdot \sqrt{9} \cdot \sqrt{6}\)

Step 4 :\(8 \sqrt{5}+2 \sqrt{6}-3 \sqrt{5}-9 \sqrt{6}\)

Step 5 :\(8 \sqrt{5}-3 \sqrt{5}+2 \sqrt{6}-9 \sqrt{6}\)

Step 6 :\(5 \sqrt{5}-7 \sqrt{6}\)

Step 7 :\(-5 \sqrt[3]{2}+\sqrt[3]{54}+5 \sqrt{2}\)

Step 8 :\(-5 \sqrt[3]{2}+\sqrt[3]{27 \cdot 2}+5 \sqrt{2}\)

Step 9 :\(-5 \sqrt[3]{2}+3 \sqrt[3]{2}+5 \sqrt{2}\)

Step 10 :\(-2 \sqrt[3]{2}+5 \sqrt{2}\)

Step 11 :\boxed{-5.97}\ and \boxed{4.55}\

From Solvely APP
Source: https://solvelyapp.com/problems/7407/

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