Question

8th grade math 1st semester exam study guide december 2
unit 1 - real number system

1. evaluate ±√169

*know the perfect squares! also, know how to find them using calculators!

1. evaluate ∛216

*know how to find cube roots using calculators!

1. express the fraction 7/8 as a decimal.
2. express the fraction 7/9 as a decimal. round to the nearest hundredth.
3. write the decimal number 0.25 as a fraction in simplest form.
4. write the decimal number 0.375 as a fraction in simplest form.
5. compare the following number using <, >, or =. √5 2.25645324
6. compare the following number using <, >, or =. √18 __ 4.121451214...

number line with points a, b, c, d at 3-4, 6-7, 7-8

1. name the point on the number line associated with the following real number: ∛15
2. name the point on the number line associated with the following real number: ∛512

unit 2 - exponents

1. simplify using exponents: 3×3×3×3×3×3×3×3
2. simplify using exponents: (-11)×(-11)×(-11)
3. simplify (hint: product rule of exponents) x²·x⁷
4. simplify (hint: product rule of exponents) 7x·2x¹¹·x¹³

Explanation:

Step1: Identify the problem type

The problem is to evaluate \( \pm\sqrt{169} \). We need to find the square roots of 169, both positive and negative.

Step2: Recall the definition of square root

A square root of a number \( a \) is a value \( x \) such that \( x^2 = a \). For \( \sqrt{169} \), we need to find a number that when squared gives 169. We know that \( 13^2 = 169 \) because \( 13\times13 = 169 \). Also, \( (-13)^2 = 169 \) because \( (-13)\times(-13)=169 \). So, the square roots of 169 are \( \pm13 \).

Answer:

\( \pm13 \)