Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply. Write your answer in simplest form. $\newline$ $\sqrt{5}(4 - \sqrt{3})$

View step-by-step help

View step-by-step help

Simplify radical expressions using the distributive property

Full solution

Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{5}(4 - \sqrt{3})

Distribute $\sqrt{5}$ : We need to distribute $\sqrt{5}$ across the terms inside the parentheses. $\sqrt{5}(4 - \sqrt{3}) = \sqrt{5} \times 4 - \sqrt{5} \times \sqrt{3}$
Multiply by $4$ : Now we multiply $\sqrt{5}$ by $4$ . $\sqrt{5} \times 4 = 4\sqrt{5}$
Multiply by $\sqrt{3}$ : Next, we multiply $\sqrt{5}$ by $\sqrt{3}$ . $\sqrt{5} \times \sqrt{3} = \sqrt{5 \times 3} = \sqrt{15}$
Combine results: Combine the two results to get the final expression. $4\sqrt{5} - \sqrt{15}$

More problems from Simplify radical expressions using the distributive property

Question

Rosie went on a hiking trip. The first day she walked

18

kilometers. Each day since, she walked

90 \%

of what she walked the day before.

\newline

What is the total distance Rosie has traveled by the end of the

10^{\text {th }}

\newline

Round your final answer to the nearest kilometer.

\newline

\mathrm{km}

Posted 4 months ago

Question

A monkey is swinging from a tree. On the first swing, she passes through an arc of

10 \mathrm{~m}

. With each swing, she passes through an arc

\frac{9}{10}

the length of the previous swing.

\newline

What is the total distance the monkey has traveled when she completes her

25^{\text {th }}

swing? Round your final answer to the nearest meter.

\newline

Posted 4 months ago

Question

S E=\frac{\sigma}{\sqrt{n}}

\newline

The given equation relates the standard error,

S E

, of a sample mean to the population standard deviation,

\sigma

, and the size of the sample,

n

. Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?

\newline

1

\newline

n=\left(\frac{\sigma}{S E}\right)^{2}

\newline

n=\frac{\sigma^{2}}{S E}

\newline

n=\sqrt{\left(\frac{\sigma}{S E}\right)}

\newline

n=\frac{\sqrt{\sigma}}{S E}

Posted 4 months ago

Question

Avery is designing a large rectangular sign. They want the sign to have an area of

2 \mathrm{~m}^{2}

\frac{4}{5} \mathrm{~m}

\newline

How tall should the sign be?

\newline

Posted 4 months ago

Question

The bacteria in a Petri dish culture are self-duplicating at a rapid pace.

\newline

The relationship between the elapsed time

t

, in minutes, and the number of bacteria,

B(t)

, in the Petri dish is modeled by the following function.

\newline

B(t)=10 \cdot 2^{\frac{t}{12}}

\newline

How many bacteria will make up the culture after

120

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

Posted 4 months ago

Question

A large brine tank containing a solution of salt and water is being diluted with fresh water.

\newline

The relationship between the elapsed time,

t

, in hours, after the dilution begins, and the concentration of salt in the tank,

S(t)

, in grams per liter

(\mathrm{g} / \mathrm{l})

, is modeled by the following function.

\newline

S(t)=500 \cdot e^{-0.25 t}

\newline

What will the concentration of salt be after

10

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

1

Posted 4 months ago

Question

After the closing of the mill, the town of Sawyerville experienced a decline in its population.

\newline

The relationship between the elapsed time,

t

, in years, since the closing of the mill, and the town's population,

P(t)

, is modeled by the following function.

\newline

P(t)=12,000 \cdot 2^{-\frac{t}{15}}

\newline

In how many years will Sawyerville's population be

9000

? Round your answer, if necessary, to the nearest hundredth.

\newline

Posted 4 months ago

Question

Carlos has taken an initial dose of a prescription medication.

\newline

The relationship between the elapsed time

t

, in hours, since he took the first dose, and the amount of medication,

M(t)

, in milligrams (

\mathrm{mg}

), in his bloodstream is modeled by the following function.

\newline

M(t)=20 \cdot e^{-0.8 t}

\newline

In how many hours will Carlos have

1 \mathrm{mg}

of medication remaining in his bloodstream?

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

Posted 4 months ago

Question

To take a taxi, it costs

\$ 3.00

plus an additional

\$ 2.00

per mile traveled. You spent exactly

\$ 20

on a taxi, which includes the

\$ 1

\newline

How many miles did you travel?

\newline

Posted 3 months ago

Question

Order the following numbers from least to greatest.

\newline

\begin{array}{l|l|l} 1.3 & \frac{5}{4} & 1 \frac{8}{25} \end{array}

Posted 3 months ago