Question

test prep

1. which of the following is not a perfect cube?

a 1
b 8
c 9
d 27

1. iris wrote a square root of 144 on a piece of paper. which one of the following must be true about the number she wrote?

a the number is 12.
b the number is $-12$.
c the number multiplied by itself equals 144.
d none of the above is true.

1. which of the following is an irrational number?

a $sqrt3{1}$
b $sqrt{2}$
c $sqrt3{27}$
d $sqrt{25}$

1. which number when squared makes 26?

a 52
b 13
c 5.5
d $sqrt{26}$

1. a square flower bed has an area of $\frac{169}{36}$ square yards. what is the perimeter of the flower bed?

$\frac{square}{square}$ yards

Explanation:

Question 11

Step1: Identify perfect cubes

A perfect cube is $n^3$ for integer $n$.

• $1=1^3$, $8=2^3$, $27=3^3$, $9$ cannot be written as $n^3$.

Question 12

Step1: Define square root

A square root of $x$ satisfies $y^2=x$.
$\sqrt{144}=\pm12$, so both 12 and -12 work, but only option C is always true.

Question 13

Step1: Classify rational/irrational

Rational numbers are fractions/integers.

• $\sqrt[3]{1}=1$, $\sqrt[3]{27}=3$, $\sqrt{25}=5$ (all rational); $\sqrt{2}$ is non-terminating, non-repeating (irrational).

Question 14

Step1: Solve for squared number

Let $x^2=26$, so $x=\sqrt{26}$.

Question 15

Step1: Find square side length

Area of square $A=s^2$, so $s=\sqrt{\frac{169}{36}}=\frac{13}{6}$

Step2: Calculate perimeter

Perimeter $P=4s=4\times\frac{13}{6}=\frac{26}{3}$

Answer:

1. C. 9
2. C. The number multiplied by itself equals 144.
3. B. $\sqrt{2}$
4. D. $\sqrt{26}$
5. $\frac{26}{3}$