QuestionAugust 26, 2025

3. 2sqrt (5)cdot 6sqrt (10) 6 3sqrt (324x^2yz^5)

3. 2sqrt (5)cdot 6sqrt (10) 6 3sqrt (324x^2yz^5)
3. 2sqrt (5)cdot 6sqrt (10)
6 3sqrt (324x^2yz^5)

Solution
4.5(302 votes)

Answer

60\sqrt{2}, 54xyz^2\sqrt{z} Explanation 1. Simplify the first expression Multiply the coefficients and the radicals separately: 2 \cdot 6 = 12 and \sqrt{5} \cdot \sqrt{10} = \sqrt{50}. Simplify \sqrt{50} to 5\sqrt{2}, so the expression becomes 12 \cdot 5\sqrt{2} = 60\sqrt{2}. 2. Simplify the second expression Simplify \sqrt{324x^{2}yz^{5}}: \sqrt{324} = 18, \sqrt{x^2} = x, \sqrt{z^5} = z^2\sqrt{z}. The expression becomes 3 \cdot 18x \cdot yz^2\sqrt{z} = 54xyz^2\sqrt{z}.

Explanation

1. Simplify the first expression<br /> Multiply the coefficients and the radicals separately: $2 \cdot 6 = 12$ and $\sqrt{5} \cdot \sqrt{10} = \sqrt{50}$. Simplify $\sqrt{50}$ to $5\sqrt{2}$, so the expression becomes $12 \cdot 5\sqrt{2} = 60\sqrt{2}$.<br /><br />2. Simplify the second expression<br /> Simplify $\sqrt{324x^{2}yz^{5}}$: $\sqrt{324} = 18$, $\sqrt{x^2} = x$, $\sqrt{z^5} = z^2\sqrt{z}$. The expression becomes $3 \cdot 18x \cdot yz^2\sqrt{z} = 54xyz^2\sqrt{z}$.
Click to rate: