Summary
This video explains how to identify rational and irrational numbers through examples, applying rules for sums and products of these types of numbers.
Highlights
Example 1: 9 + √45
00:00:00
The number 9 is rational. √45 can be simplified to 3√5. Since √5 is irrational, 3√5 is also irrational. The sum of a rational number (9) and an irrational number (3√5) results in an irrational number.
Example 2: √45 / 6√5
00:02:13
Simplify √45 to √9 * √5, which is 3√5. The expression becomes (3√5) / (6√5). The √5 terms cancel out, leaving 3/6, which simplifies to 1/2. Since 1/2 is a ratio of two integers, the number is rational.
Example 3: 3 * √9
00:03:12
Since 9 is a perfect square, √9 is 3. So, the expression becomes 3 * 3, which equals 9. As 9 is an integer, it can be written as 9/1, making it a rational number.