Solve \sqrt { 5 } ( 5 \sqrt { 7 } + 6 \sqrt { 10 } )

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Question

$$\sqrt { 5 } ( 5 \sqrt { 7 } + 6 \sqrt { 10 } )$$

$5\left(\sqrt{35}+6\sqrt{2}\right)\approx 72.006805787$

Use the distributive property to multiply $\sqrt{5}$ by $5\sqrt{7}+6\sqrt{10}$.

$$5\sqrt{5}\sqrt{7}+6\sqrt{5}\sqrt{10}$$

To multiply $\sqrt{5}$ and $\sqrt{7}$, multiply the numbers under the square root.

$$5\sqrt{35}+6\sqrt{5}\sqrt{10}$$

Factor $10=5\times 2$. Rewrite the square root of the product $\sqrt{5\times 2}$ as the product of square roots $\sqrt{5}\sqrt{2}$.

$$5\sqrt{35}+6\sqrt{5}\sqrt{5}\sqrt{2}$$

Multiply $\sqrt{5}$ and $\sqrt{5}$ to get $5$.

$$5\sqrt{35}+6\times 5\sqrt{2}$$

Multiply $6$ and $5$ to get $30$.

$$5\sqrt{35}+30\sqrt{2}$$