Question

1. simplify $(-2)^2 + 5$

a $-6$ c $9$
b $-3$ d $12$

1. is the expression rational or irrational?

$\frac{7}{8}+\sqrt{25}$

1. is the expression rational or irrational?

$-10\sqrt{5}$

1. which triangle has a perimeter that is an irrational number?

a sides 2 cm, $\sqrt{17}$ cm, and 4 cm
b sides 3 cm, 13 cm, and 14 cm
c side 3 cm, 4 cm, and 5 cm
d side 1 cm, $\sqrt{4}$ cm, and 3 cm

Explanation:

Step1: Evaluate the squared term

$(-2)^2 = 4$

Step2: Add the constant term

$4 + 5 = 9$

1. $\frac{7}{8}$ is a rational number (fraction of integers).
2. $\sqrt{25} = 5$, which is a rational number (integer).
3. The sum of two rational numbers is rational.

1. $\sqrt{5}$ is an irrational number (cannot be written as a fraction of integers).
2. Multiplying an irrational number by a non-zero rational number (-10) results in an irrational number.

Step1: Calculate perimeter of Option A

$2 + \sqrt{17} + 4 = 6 + \sqrt{17}$
$\sqrt{17}$ is irrational, so the sum is irrational.

Step2: Calculate perimeter of Option B

$3 + 13 + 14 = 30$ (rational integer)

Step3: Calculate perimeter of Option C

$3 + 4 + 5 = 12$ (rational integer)

Step4: Calculate perimeter of Option D

$\sqrt{4}=2$, so $1 + 2 + 3 = 6$ (rational integer)

Answer:

C. 9

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