Multiply. Write your answer in simplest form. sqrt 5(8 - sqrt 2) ______

Distribute sqrt(5): Distribute sqrt(5) to both terms inside the parentheses. sqrt(5)(8 - sqrt(2)) = sqrt(5)*8 - sqrt(5)*sqrt(2)Multiply by 8: We have: sqrt(5) × 8 = 8sqrt(5) This is a straightforward multiplication of a radical and an integer.Multiply by -sqrt(2): Next, we have: sqrt(5) × (-sqrt(2)) = -sqrt(5*2) = -sqrt(10) This is the product of two radicals, which can be combined under a single radical sign.Combine results: Combine the results from the previous steps to get the final simplified expression: 8sqrt(5) - 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. $\newline$ $\sqrt{5}(8 - \sqrt{2})$

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{5}(8 - \sqrt{2})

Distribute $\sqrt{5}$ : Distribute $\sqrt{5}$ to both terms inside the parentheses. $\sqrt{5}(8 - \sqrt{2}) = \sqrt{5}\times8 - \sqrt{5}\times\sqrt{2}$
Multiply by $8$ : We have: $\newline$ $\sqrt{5} \times 8 = 8\sqrt{5}$ $\newline$ This is a straightforward multiplication of a radical and an integer.
Multiply by $-\sqrt{2}$ : Next, we have: $\sqrt{5} \times (-\sqrt{2}) = -\sqrt{5\times2} = -\sqrt{10}$ This is the product of two radicals, which can be combined under a single radical sign.
Combine results: Combine the results from the previous steps to get the final simplified expression: $8\sqrt{5} - \sqrt{10}$