<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B40%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20" id="TexFormula1" title=" \

All categories

alina1380 [7]

3 years ago

frac{ \sqrt{40} }{ \sqrt{3} } " alt=" \frac{ \sqrt{40} }{ \sqrt{3} } " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

storchak [24]3 years ago

5 0

Answer:

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }$

Step-by-step explanation:

Given

$\frac{ \sqrt{40} }{ \sqrt{3} }$

Required

Simplify

$\frac{ \sqrt{40} }{ \sqrt{3} }$

Rationalize:

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40} }{ \sqrt{3} }*\frac{ \sqrt{3} }{ \sqrt{3} }$

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40*3} }{ \sqrt{3*3} }$

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ \sqrt{9} }$

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ 3 }$

Expand the numerator

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4*30} }{ 3 }$

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4}*\sqrt{30} }{ 3 }$

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ 2*\sqrt{30} }{ 3 }$

$\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }$

You might be interested in

jacob wants to buy packets of fruit juice. on tuesday, he buys 8 packets of orange and 6 packets of Apple the packets make a tot

ioda

Answer:

Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

Step-by-step explanation:

Let number of cups of juice in each packet of orange be 'x'.

Let number of cups of juice in each pack of apples be 'y'.

Given:

On Tuesday;

Number of packets of oranges = 8

Number of packets of apples = 6 packets.

Amount of fruit juice = 34 cups

So we can say that;

Amount of fruit juice is equal to sum of Number of packets of oranges multiplied by number of cups of juice in each packet of orange and Number of packets of apples multiplied by number of cups of juice in each pack of apples.

framing in equation form we get;

$8x+6y=34 \ \ \ \ equation \ 1$

On Wednesday;

Number of packets of oranges = 14

Number of packets of apples = 6

Amount of fruit juice = 46 cups

So we can say that;

framing in equation form we get;

$14x+6y=46 \ \ \ \ equation \ 2$

Now Subtracting equation 1 from equation we get;

$14x+6y-(8x+6y)=46-34\\\\14x+6y-8x-6y=12\\\\6x=12$

Now dividing both side by 6 we get;

$\frac{6x}{6}=\frac{12}{6}\\\\x=2\ cups$

Now we will substitute the value of 'x' in equation 1 we get;

$8x+6y=34\\\\8\times2+6y=34\\\\16+6y=34$

Subtracting both side by 16 we get;

$16+6y-16=34-16\\\\6y= 18$

Now dividing both side by 6 we get;

$\frac{6y}{6}=\frac{18}{6}\\\\y=3$

Hence Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

5 0

3 years ago

The Stock Market nadia is a stockbroker. earns % commission each week. Last week, she earned $ in commission. How much were h

Bond [772]

Hi my name is nadia so i felt like answering this lol. this question is missing a lot of things. it doesn’t look like i can answer it.

5 0

2 years ago

The cost of a large pizza is given by c = 0.50t + 18, where c is the total cost and t is the number of toppings. The cost of a m

Mashutka [201]

The toppings would still cost 0.50 each (since it is just toppings)

The large pizza costs $18 if you do not have any toppings
The medium costs half of the large

18/2 = 9

The medium costs $9 without any toppings, so your new equation will be:

c = 0.50t + 9

hope this helps

6 0

3 years ago

Read 2 more answers

The garden hose at Andre's house can fill a 5-gallon bucket in 2 minutes. The hose at his next-door neighbor's house can fill a

mina [271]

Answer:

The time it would take them to fill 750 gallons

= 200 minutes or 3 hours 20 minutes

Step-by-step explanation:

Step 1 :

We calculate the rate at which the hoses fill for Andre and His neighbor

For Andre

The garden hose at Andre's house can fill a 5-gallon bucket in 2 minutes.

The rate is calculated as:

5 gallon/2 minutes

= 2.5 gallons/minute

For His neighbor

The hose at his next-door neighbor's house can fill a 10-gallon bucket in 8

minutes.

= 10 gallon/8 minutes

= 1.25 gallon/minute

Step 2

Hence:

If they use both their garden hoses at the same time, and the hoses continue working at the same rate, the sum of their rate =

2.5 + 1.25 = 3.75 gallons per minute.

Step 3

The time it would take them to fill 750 gallons =

750 gallons ÷ 3.75 gallons per minute

= 200 minutes

= 3 hours 20 minutes

6 0

2 years ago

Thomas reads 2/9 of a book on Monday and 1/6 of it on Tuesday. He reads twice as many pages on Wednesday as on Tuesday. What fra

dezoksy [38]

1/18 is left. Thomas has 1/18 left of his book. How? What denominator can 9&6 relate to? 54? Sure, but it could be lower. How about 18? Ok. We have 18 because 9x2 and 6x3 both equal 18... 2/9 becomes 4/18 because 18 divided by 9 is 2. You multiply 2 with the two from 2/9. 1/6 becomes 3/18 because 18 divided by 6 is 3. You then multiply 3 with the one from 1/6. Put it together and TA-DA... Your answer is 1/18

8 0

3 years ago