1) the types of number are the negative integers (e.g √-1 √-3 <span>√-5 are not defined)
2) the answer is No, proof: 2x</span>√-1 is not defined because <span>√-1 doesn't exist
3) the answer is No, proof: </span>√-1 - 3 is not defined because √-1 doesn't exist
4) the answer is Yes, proof: (√-1 )²= -1 this is a real number
5) the answer is No, proof: (√-1 )^3= (√-1 )²(√-1 )= - 1(√-1 ), and - 1(√-1 ) is not defined because √-1 doesn't exist
6) the result would be defined with the following cases:
√-1+n, n>1
√-1xn, n<0
√-1/n, n<0
7) the result would not be defined with the following cases:
√-1+n, n<0
√-1xn, n>0
√-1/n, n>0
8) to square <span>3 + √-1, I use the method of complex number
i²= -1, it implies i= </span>√-1
so 3+√-1=3+i, and then (3+√-1)²=(3+i)²= 9 -1+6i= 8-i= 8-√-1
9) it is used for finding complex roots of a number
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 have to first mess around with the first shape, ABCD, and split that into a rectangle and a right triangle. once you do that, it's pretty painstaking, but simple.
if you look at it you can tell that EFGH is just half the size, but the same ratios and everything.
So, you would just take every perimeter measurement from ABCD, and divide it by two and then sum them together.
2.5 + 1.5 + 4.0 + 2.0 = 10
