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Question

# Use the duck principle to show that each equation is true. a. $\sqrt{125} \cdot \sqrt{5} = 5$ b. $\sqrt{18} \cdot \sqrt{12} = 6$ c. $\dfrac{\sqrt{128}}{\sqrt{16}} = \sqrt{8}$ d. $\sqrt{100} = \sqrt{10}$ e. $\sqrt{4} \cdot \sqrt{3} = \sqrt{48}$

Solution

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$(a)\ \sqrt{125}\ \cdot \sqrt{5}$

From the rule that $\sqrt{x}\ \cdot \sqrt{y} = \sqrt{xy}$

We get $\sqrt{125}\ \cdot \sqrt{5} = \sqrt{625}$

Also $625 = 5^4$

So $5$ is the fourth root of 625.

Thus $\sqrt{125}\ \cdot \sqrt{5} = \sqrt{625} = 5$

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