Question

PLEASE HELP!!

1) If X^2=40, what is the value of X?
A) +- 80
B) +- 20
C) +- square root of 80
D) +- square root of 40


2) Solve X^2= -169
A) Undefined
B) 13
C) +- 13
D) -13


3) A square rug covers 79 square feet of floor. What is the approximate length of one side of the rug?(approximate to the nearest hundredth foot)
A) 8.86 feet
B) 8.87 feet
C) 8.88 feet
D) 8.89 feet

Answer 1

1. D

2. A

3. D

Explanation:

1.

To solve the equation
`x^2=40`, we need to take "square root" of both the sides so we can isolate the variable "x".

Note: When taking square root, we need both positive(+) and negative(+) value as both positive & negative value's square is same.

Thus,

`x^2=40\\√(x^2) =+-√(40)\\ x=+-√(40)`

Answer choice D is right.

2.

So we need to take square root of both the sides to isolate the variable x and solve. Thus:

`x^2=-169\\√(x^2)=√(-169)\\  x=√(-169)`

Now, we CANNOT TAKE THE SQUARE ROOT OF A NEGATIVE NUMBER. Hence, we cannot solve this. It is UNDEFINED.

Answer choice A is right.

3.

A square has an area given by
`s^2`, where s is side length.

Equating the area to 79 and solving for s gives us the length of one side of the rug (remember to take square root of both sides to isolate s):

`s^2=79\\√(s^2)=√(79) \\ s=√(79) =8.89`

Note: we disregarded the negative value of -8.89 because length CANNOT BE NEGATIVE!

Hence, answer choice D is right.