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 the definition of a rational number?

Provide examples of rational numbers and explain their decimal representations.

Explain the difference between rational and irrational numbers.

How can the sum of 3 times the square root of 2 and 4 times the square root of 2 be simplified?

What is the decimal representation of 7 times the square root of 2, and what does it indicate about the number?