Regents Exam: Algebra I August 2016 (Problem 29 of 37)

The video tutorial addresses problem number 29, which asks whether the sum of 3 times the square root of 2 and 4 times the square root of 2 is rational or irrational. It explains the difference between rational and irrational numbers, providing examples and characteristics of each. Rational numbers can be expressed as a ratio of two integers and may have terminating or repeating decimal representations. In contrast, irrational numbers cannot be expressed as such ratios and have non-terminating, non-repeating decimals. The tutorial concludes by solving the problem, showing that the sum is 7 times the square root of 2, an irrational number, as its decimal representation is non-terminating and non-repeating.

What is a rational number?

• A number that can be expressed as a ratio of two integers

• A number that is always positive

• A number that cannot be expressed as a ratio of two integers

• A number with a non-terminating, non-repeating decimal

Which of the following is an example of a rational number with a repeating decimal?

• Square root of 2

• Pi

• 0.25

• 0.333...

What distinguishes an irrational number from a rational number?

• Its decimal representation does not repeat or terminate

• It is always a whole number

• It can be written as a ratio of two integers

• It has a repeating decimal pattern

What is the sum of 3 times the square root of 2 and 4 times the square root of 2?

• 7

• 14 square root of 2

• 7 square root of 2

• 14

Why is the sum of 3 square root 2 and 4 square root 2 considered irrational?

• Because it is a whole number

• Because its decimal representation does not terminate or repeat

• Because its decimal representation terminates

• Because it can be expressed as a ratio of two integers