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img of Simplify. √20w + √45w Assume that the variable represents a...

Question: Simplify. √20w + √45w Assume that the variable represents a positive real number.

Simplify. √20w + √45w Assume that the variable represents a positive real number.

Solution

Simplify the expression: \[ \sqrt{20w} + \sqrt{45w} \] First, simplify each square root term separately. For \(\sqrt{20w}\), break it down: \[ \sqrt{20w} = \sqrt{4 \cdot 5 \cdot w} = \sqrt{4} \cdot \sqrt{5} \cdot \sqrt{w} = 2\sqrt{5w} \] For \(\sqrt{45w}\), break it down: \[ \sqrt{45w} = \sqrt{9 \cdot 5 \cdot w} = \sqrt{9} \cdot \sqrt{5} \cdot \sqrt{w} = 3\sqrt{5w} \] Combine the simplified terms: \[ 2\sqrt{5w} + 3\sqrt{5w} = (2 + 3)\sqrt{5w} = 5\sqrt{5w} \] The simplified expression is: \[ 5\sqrt{5w} \]

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