Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers.

$-4\sqrt{5}(2\sqrt{5}+4\sqrt{12})$

emancipezN
2021-09-09
Answered

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers.

$-4\sqrt{5}(2\sqrt{5}+4\sqrt{12})$

You can still ask an expert for help

Brittany Patton

Answered 2021-09-10
Author has **100** answers

To find:

The product of$-4\sqrt{5}(2\sqrt{5}+4\sqrt{12})$ and express answer in simplest radical form:

Concept used:

Distributive property:

$a(b+c)=ab+ac$

Radical property:

$\sqrt{a\times a}=a$

$\sqrt{a}\times \sqrt{b}=\sqrt{ab}$

Calculation:

The product of$-4\sqrt{5}(2\sqrt{5}+4\sqrt{12})$ can be obtained as,

$-4\sqrt{5}(2\sqrt{5}+4\sqrt{12})=-4\sqrt{5}\cdot 2\sqrt{5}-4\sqrt{5}\cdot 4\sqrt{12}$

$=-8\sqrt{5\cdot 5}-16\sqrt{5\cdot 12}$

$=-8\cdot 5-16\sqrt{5\cdot 2\cdot 2\cdot 3}$

$=-40-32\sqrt{15}$

Thus, the product of$-4\sqrt{5}(2\sqrt{5}+4\sqrt{12})$ is $-40-32\sqrt{15}$

The product of

Concept used:

Distributive property:

Radical property:

Calculation:

The product of

Thus, the product of

asked 2020-11-22

Radical and Exponents Simplify the expression

asked 2022-04-04

$7\sqrt{5}+5\sqrt{5}\ufeff=$?

asked 2022-05-07

What is $2\sqrt{2}$ plus $5\sqrt{2}$?

asked 2020-11-10

If $s\ge 0$ , then $\surd {s}^{2}$ is equal to

O A. 0

O B. 1

O c. −s

O D. s

O A. 0

O B. 1

O c. −s

O D. s

asked 2021-10-18

Rewrite with rational exponents:

asked 2021-09-19

Evaluate the expression.

$\sqrt{2}\sqrt{50}$

asked 2022-05-17

Compute $$31\sqrt{1014}+44\sqrt{486}$$.