ANSWER TO QUESTION 1
A rational number is any number that can be written in the form,, where
and
are integers and
.
We can rewrite .
Therefore option A is a rational number.
Option B is obviously a rational number because it is already in the form .
Option C cannot be written in the form because the decimal place does not repeat or recur and it does not terminate also.
Therefore is not a rational number.
As for option D, the decimal places recurs or repeats and it does not terminate. We can rewrite in the form,.
hence it is a rational number.
ANSWER TO QUESTION 2
Yes is a perfect square.
All numbers whose square roots are perfect squares are rational numbers.
If we raise we get
.
In order words if we take the square root of we get a rational number.
That is
ANSWER TO QUESTION 3
Let the length from the wall to the base of the ladder be m.
The from Pythagoras Theorem,
This implies that,
We add the additive inverse of to both sides to obtain,
We take the positive square root of both sides to obtain,
.
The correct answer is A.
ANSWER TO QUESTION 4
We wan to estimate .
The highest perfect square that can be found in is
.
We rewrite to obtain,
.
We now split the square root sign to obtain,
.
.
.
.
ANSWER TO QUESTION 5.
The statement, every rational number is q square root is false.
We only need at least a counterexample to show that, the above statement is false.
Let be any real number.
Then , where
and
are integers.
This implies that
Base on this final equation, can only be an integer if
is a perfect number. Hence not every rational number is a square root because some numbers aren't perfect squares.
The correct answer is C
ANSWER TO QUESTION 6.
To find the translation vector that maps the blue rectangle on the red rectangle, we draw a vector connecting any two corresponding points as shown in the diagram.
The vector has horizontal component of and a vertical component of
.
Therefore the mapping is . The correct answer is D.
ANSWER TO QUESTION 7
Figure A accurately represents the Pythagorean Theorem because
This implies that
We can see that the hypotenuse square is equal to the sum of the squares of the lengths of the two shorter legs.
Recall that, are Pythagorean triples.
