Multiply. Write your answer in simplest form. sqrt 5(-8 + sqrt 3) ______

Distribute sqrt(5): Distribute sqrt(5) to both terms inside the parentheses. We have the expression sqrt(5)(-8 + sqrt(3)), which requires us to multiply sqrt(5) with each term inside the parentheses separately. sqrt(5) * (-8) + sqrt(5) * sqrt(3)Multiply by -8: Multiply sqrt(5) by -8. When we multiply a square root by a real number, we simply multiply the number outside the radical with the real number. sqrt(5) * (-8) = -8 * sqrt(5)Multiply by sqrt(3): Multiply sqrt(5) by sqrt(3). When we multiply two square roots together, we multiply the numbers inside the radicals. sqrt(5) * sqrt(3) = sqrt(5 * 3) = sqrt(15)Combine results: Combine the results from Step 2 and Step 3. We have -8 * sqrt(5) from Step 2 and sqrt(15) from Step 3. Combining these gives us the final simplified expression. -8 * sqrt(5) + sqrt(15)

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{5}(-8 + \sqrt{3})$

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Algebra 2

Simplify radical expressions using the distributive property

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{5}(-8 + \sqrt{3})

Distribute $\sqrt{5}$ : Distribute $\sqrt{5}$ to both terms inside the parentheses. $\newline$ We have the expression $\sqrt{5}(-8 + \sqrt{3})$ , which requires us to multiply $\sqrt{5}$ with each term inside the parentheses separately. $\newline$ $\sqrt{5} \times (-8) + \sqrt{5} \times \sqrt{3}$
Multiply by $-8$ : Multiply $\sqrt{5}$ by $-8$ . When we multiply a square root by a real number, we simply multiply the number outside the radical with the real number. $\sqrt{5} \times (-8) = -8 \times \sqrt{5}$
Multiply by $\sqrt{3}$ : Multiply $\sqrt{5}$ by $\sqrt{3}$ . $\newline$ When we multiply two square roots together, we multiply the numbers inside the radicals. $\newline$ $\sqrt{5} \times \sqrt{3} = \sqrt{5 \times 3} = \sqrt{15}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have $-8 \times \sqrt{5}$ from Step $2$ and $\sqrt{15}$ from Step $3$ . Combining these gives us the final simplified expression. $\newline$ $-8 \times \sqrt{5} + \sqrt{15}$