Unit 1 Quiz 2: Rational vs. Irrational & Radical Operations

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.
• Irrational; The sum of a rational and an irrational is always irrational.
• Rational; The product of two rationals is always rational.
• Irrational; The product of a nonzero rational and an irrational is always irrational.

A REPEATING decimal is what type of number?

• Rational 
• Irrational

Which of the following number is rational?

• $\sqrt{127}$

• $\pi$

• $2.5$

• $8.98763...$

Determine which of the following examples is irrational.

• A fraction whose denominator is larger than its numerator

• A decimal that never ends but repeats

• A perfect cube root

• A decimal that never ends and never repeats

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.
• Irrational; The sum of a rational and an irrational is always irrational.
• Rational; The product of two rationals is always rational.
• Irrational; The product of a nonzero rational and an irrational is always irrational.

Simplify:
√10 ⋅ √45

• 3√50
• 8√2
• √450
• 15√2

Simplify √72

• 7√9
• 4√6
• 6√2
• 3√4

Simplify
3√2 - 3√18

•  -4√8
• 4√9-6√3
• 5√12
• -6√2

Simplify
-2√5+3√20

• -2√8
• -6√36
• -6√-12
•  4√5

Simplify: 4√6 - 3√24

• -2√6
• 3√6
• 10√6
• -4√6