Which of the following are examples of irrational numbers? Select all that apply.
√4 + √16
√5 + √36
√9 + √24
2 x √4
√49 x √81
3√12
√5 + √36
√9 + √24
√49 x √81
3√12
can you explain?
Sure! To determine whether a number is irrational, we need to check if it can be expressed as a fraction or if it has a repeating or terminating decimal expansion.
Let's go through each option:
1) √4 + √16: √4 is equal to 2, and √16 is equal to 4. So this expression can be simplified as 2 + 4, which equals 6. 6 is a rational number because it can be expressed as 6/1. Therefore, this option is not an example of an irrational number.
2) √5 + √36: √5 is an irrational number because it cannot be expressed as a fraction and its decimal expansion does not repeat or terminate. √36 is equal to 6, which is a rational number because it can be expressed as 6/1. Therefore, this option is an example of an irrational number.
3) √9 + √24: √9 is equal to 3, and √24 is an irrational number. Therefore, this option is also an example of an irrational number.
4) 2 x √4: √4 is equal to 2, so this expression simplifies to 2 x 2, which is equal to 4. 4 is a rational number because it can be expressed as 4/1. Therefore, this option is not an example of an irrational number.
5) √49 x √81: √49 is equal to 7, and √81 is equal to 9. So this expression simplifies to 7 x 9, which is equal to 63. 63 is a rational number because it can be expressed as 63/1. Therefore, this option is not an example of an irrational number.
6) 3√12: √12 is an irrational number. So this expression simplifies to 3 x √12, which remains irrational. Therefore, this option is an example of an irrational number.
In summary, the examples of irrational numbers are:
- √5 + √36
- √9 + √24
- 3√12