1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
faust18 [17]
3 years ago
5

If 18√8 - 8 √18 = √n, what is n?

Mathematics
1 answer:
Yuliya22 [10]3 years ago
5 0

Answer:

n=288

Step-by-step explanation:

Rewrite the equation as  

√

n

=

18

√

8

−

8

√

18

.

√

n

=

18

√

8

−

8

√

18

To remove the radical on the left side of the equation, square both sides of the equation.

√n

2

=

(

18

√

8

−

8

√

18

)

2

Simplify each side of the equation.  

Use  

n

√

a

x

=

a

x

n

to rewrite  

√

n  as  n

1

2

.

(

n

1

2

)

2

=

(

18

√

8

−

8

√

18

)

2

Simplify  

(

n

1

2

)

2

.  

Multiply the exponents in  

(

n

1

2

)

2

.  

Apply the power rule and multiply exponents,  

(

a

m)n

=

a

m

n

.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

)

2

Cancel the common factor of  2  

Cancel the common factor.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

)

2

Rewrite the expression.

n

1

=

(

18

√

8

−

8

√

18

)

2

Simplify.

n

=

(

18

√

8

−

8

√

18

)

2

Simplify  

(

18

√

8

−

8

√

18

)

2

Simplify each term.

Rewrite  

8  as  2

2

⋅

2

.  

Factor  

4  out of  8  

n

=

(

18

√

4

(

2

)

−

8

√

18

)

2

Rewrite  

4  as  2

2  

n

=

(

18√

2

2

2

−

8

√

18

)

2

Pull terms out from under the radical.

n

=

(

18

(

2

√

2

)

−

8

√

18

)

2

Multiply  

2  by  18  

n

=

(

36

√

2

−

8

√

18

)

2

Rewrite  

18

as  

3

2

⋅

2

.

Factor  

9

out of  

18

.

n

=

(

36

√

2

−

8

√

9

(

2

)

)

2

Rewrite  

9

as  

3

2

.

n

=

(

36

√

2

−

8

√

3

2

⋅

2

)

2

Pull terms out from under the radical.

n

=

(

36

√

2

−

8

(

3

√

2

)

)

2

Multiply  

3

by  

−

8

.

n

=

(

36

√

2

−

24

√

2

)

2

Simplify terms.

Subtract  

24

√

2

from  

36

√

2

.

n

=

(

12

√

2

)

2

Simplify the expression.

Apply the product rule to  

12

√

2

.

n

=

12

2

√

2

2

Raise  

12

to the power of  

2

.

n

=

144

√

2

2

Rewrite  

√

2

2

as  

2

.

Use  

n

√

a

x

=

a

x

n

to rewrite  

√

2

as  

2

1

2

.

n

=

144

(

2

1

2

)

2

Apply the power rule and multiply exponents,  

(

a

m

)

n

=

a

m

n

.

n

=

144

⋅

2

1

2

⋅

2

Combine  

1

2

and  

2

.

n

=

144

⋅

2

2

2

Cancel the common factor of  

2

.

Cancel the common factor.

n

=

144

⋅

2

2

2

Rewrite the expression.

n

=

144

⋅

2

1

Evaluate the exponent.

n

=

144

⋅

2

Multiply  

144

by  

2

.

n

=

288

You might be interested in
Each floor of a building is 13.6 feet tall. If the height of the building is 108.8 feet, how many floors does the building have?
exis [7]
The answer is 8 floors
3 0
3 years ago
Read 2 more answers
The cost of coffee is determined by the type of coffee beans that are mixed together. The cost of a local mix of Arabica and Rob
Yuki888 [10]
250 pounds of Robusta beans.
3 0
3 years ago
Read 2 more answers
HELP ASAP ILL GIVE BRAINLYIST
Ratling [72]

Answer:

################

Step-by-step explanation:

6 0
3 years ago
Can someone help me, i cant find the anwser
Aloiza [94]

The range of the given function is represented by  {-6,-4,2}.

<h3>Domain and Range</h3>

The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

Here, you need to replace the given domain values in the equation: f(x)=x-4. The question gives that the domain is represented by: -2 ,0 ,2 .

Thus,

For x=-2, you have:

f(x)= x-4

f(x)= -2-4

f(x)= -6

For x=0, you have:

f(x)= 0-4

f(x)= 0-4

f(x)= -4

For x=2, you have:

f(x)= x-4

f(x)= 2-4

f(x)= -2

Therefore, the range of the given function is {-6,-4,2}

Learn more about the range here:

brainly.com/question/10197594

#SPJ1

5 0
2 years ago
Please help me now please
Y_Kistochka [10]

Answer:

surface area is 46

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Let f(x)=2x^3-4x+1. Fill in the blank with the number of times the output value (y) occurs for input values of x between -3 and
    5·1 answer
  • The dot plot below shows 4 data points with a mean of 6. mc001-1.jpg What is the absolute deviation at 2? –8 –4 4 8
    15·2 answers
  • Alex needs to buy compressed air to fill empty cylindrical tanks for his tire store. Each tank is 12 feet deep and has a radius
    6·1 answer
  • I think it's 65° is it correct??​
    5·2 answers
  • What is the mean of the following data values? 53,71,89,10,87
    10·1 answer
  • Find the integer that lies between <img src="https://tex.z-dn.net/?f=%24%5Csqrt%5B3%5D%7B-45%7D%24%20and%20%24%5Csqrt%5B3%5D%7B-
    9·1 answer
  • Need help asap please
    7·1 answer
  • Caroline owns 3 fewer T shirts than chase. Let k Represent the number of chase’s T shirt. What expression can be used? A. 3k B.
    13·1 answer
  • After sales tax a 33 dollar photo album cost 35.97 dollars. What is the sales tax percentage
    13·1 answer
  • 15. What is the value of x?<br> x°<br> (x + 10)°<br> (3x - 5)°<br> X =
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!