Given:
Expression is

To prove:
If r is any rational number, then
is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,

It can be written as

Now,
3, -2 and 4 are rational numbers by property 1.
is rational by Property 3.
are rational by Property 3.
is rational by property 2.
So,
is rational.
Hence proved.
Answer:
C
Step-by-step explanation:
8i
√-64 = i√64 = 8i
Answer:
The first one luv
Step-by-step explanation:
Answer:
The missing side length is 3 units long.
Step-by-step explanation:
Use the Pythagorean Theorem where c²=a²+b²,
c=2√3, c²=12
a²=√3, a²=3
Solving for the missing side yields a side length of 3.