Multiply. Write your answer in simplest form. -sqrt 2(3 + sqrt 5) ______

Distribute -sqrt(2): Distribute -sqrt(2) to both terms inside the parentheses. -sqrt(2)(3 + sqrt(5)) = -sqrt(2)*3 + -sqrt(2)*sqrt(5)Multiply -sqrt(2) by 3: Multiply -sqrt(2) by 3. -sqrt(2) * 3 = -3sqrt(2)Multiply -sqrt(2) by sqrt(5): Multiply -sqrt(2) by sqrt(5). -sqrt(2) * sqrt(5) = -sqrt(2 * 5) = -sqrt(10)Combine results: Combine the results from Step 2 and Step 3. -3sqrt(2) + -sqrt(10) = -3sqrt(2) - sqrt(10)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply. Write your answer in simplest form. $\newline$ $-\sqrt{2}(3 + \sqrt{5})$

View step-by-step help

Home

Math Problems

Algebra 2

Simplify radical expressions using the distributive property

Full solution

Q. Multiply. Write your answer in simplest form.

\newline

-\sqrt{2}(3 + \sqrt{5})

Distribute $-\sqrt{2}$ : Distribute $-\sqrt{2}$ to both terms inside the parentheses. $-\sqrt{2}(3 + \sqrt{5}) = -\sqrt{2}\cdot 3 + -\sqrt{2}\cdot \sqrt{5}$
Multiply $-\sqrt{2}$ by $3$ : Multiply $-\sqrt{2}$ by $3$ . $\newline$ $-\sqrt{2} \times 3$ $\newline$ $= -3\sqrt{2}$
Multiply $-\sqrt{2}$ by $\sqrt{5}$ : Multiply $-\sqrt{2}$ by $\sqrt{5}$ . $\newline$ $-\sqrt{2} \times \sqrt{5}$ $\newline$ = $-\sqrt{2 \times 5}$ $\newline$ = $-\sqrt{10}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $-3\sqrt{2} + -\sqrt{10}$ $\newline$ = $-3\sqrt{2} - \sqrt{10}$