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