Which of the following results in a sum or a product that is rational? Choose all that apply. 4.22̅̅̅̅ x 2.1
√25 x √16
√2 x √5
2 + 7
∏ x 5
√25 x √16
√2 x √5
2 + 7
To determine which of the given options result in a sum or product that is rational, we need to check if the numbers involved are rational or irrational.
1. 4.22̅̅̅̅ x 2.1:
The number 4.22̅̅̅̅ is a repeating decimal, which means it is an irrational number. The irrational number multiplied by a rational number (2.1) will yield an irrational number. Therefore, this option does not result in a sum or product that is rational.
2. √25 x √16:
Both √25 and √16 are square root expressions of perfect squares, which means they are rational numbers. The product of two rational numbers is also rational. Therefore, this option results in a sum or product that is rational.
3. √2 x √5:
Both √2 and √5 are square root expressions of prime numbers, which means they are irrational numbers. The product of two irrational numbers is also irrational. Therefore, this option does not result in a sum or product that is rational.
4. 2 + 7:
Both 2 and 7 are integers, which means they are rational numbers. The sum of two rational numbers is also rational. Therefore, this option results in a sum or product that is rational.
5. ∏ x 5:
∏ represents the mathematical constant pi, which is an irrational number. The irrational number multiplied by a rational number (5) will yield an irrational number. Therefore, this option does not result in a sum or product that is rational.
In summary, the options that result in a sum or product that is rational are:
- √25 x √16
- 2 + 7