Question

Part A: Use the properties of exponents to explain why is called the fifth root of 18.

1. What property refers to roots and fractional powers?

My Answer: Rule of exponents

2. How does it apply to 18^1/5?
If you multiply 18^1/5 by itself 5 times, you get 18.

Part B: The length of a rectangle is 2 units and its width is √2 unit. Is the area of the rectangle rational or irrational? Justify your answer.

1. What is the formula of the area of a rectangle? L x W

2. Plug and Chug your answer: 2x√2 2√2.

3) Is the answer rational or irrational? Irrational

Answer 1

1 and 2 look fine

There is nothing you can multiply sqrt 2 by to get a rational number but sqrt 2 or a multiple thereof

L * W yes

4*2 x = 8 x

as we said above if you multiply sqrt 2 by sqrt 2 it comes out a perfectly rational 2
HOWEVER, you better do it symbolically with sqrt 2, not a calculation rounded off.

Answer 2

I'm confused what you mean by 3? I was thinking Irrational because you can not write as a ratio.??

Answer 3

sqrt 2 * sqrt 2 = 2 = 2/1

you can not write sqrt 2 as a ratio of integers
but you certainly can write 2 as a ratio
and 2 is sqrt 2 * sqrt 2 by definition

However do not try to write
1.41 etc * 1.41 etc as a ratio