Solve \sqrt { 3 } ( 3 \sqrt { 15 } + 4 \sqrt { 5 } )

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Question

$$\sqrt { 3 } ( 3 \sqrt { 15 } + 4 \sqrt { 5 } )$$

$4\sqrt{15}+9\sqrt{5}\approx 35.616545182$

Use the distributive property to multiply $\sqrt{3}$ by $3\sqrt{15}+4\sqrt{5}$.

$$3\sqrt{3}\sqrt{15}+4\sqrt{3}\sqrt{5}$$

Factor $15=3\times 5$. Rewrite the square root of the product $\sqrt{3\times 5}$ as the product of square roots $\sqrt{3}\sqrt{5}$.

$$3\sqrt{3}\sqrt{3}\sqrt{5}+4\sqrt{3}\sqrt{5}$$

Multiply $\sqrt{3}$ and $\sqrt{3}$ to get $3$.

$$3\times 3\sqrt{5}+4\sqrt{3}\sqrt{5}$$

Multiply $3$ and $3$ to get $9$.

$$9\sqrt{5}+4\sqrt{3}\sqrt{5}$$

To multiply $\sqrt{3}$ and $\sqrt{5}$, multiply the numbers under the square root.

$$9\sqrt{5}+4\sqrt{15}$$