Answer:
b) the product of two rational numbers rational
Step-by-step explanation:
A rational number can be defined as a number that has a numerator or a denominator. This means that a rational number exists as a fraction e.g 2/3, 6/7 e.t.c
An irrational number is a number that cannot exist as a fraction or as a ration between two numbers. Irrational number can be expressed in decimal format that continues and keeps continuing.
And example of an irrational number is : √2, √5, √7 e.t.c
We were given 4 options above.
a) the product of two irrational numbers is irrational
The product of two irrational number can give us both a rational number and an irrational number. For example,
√2 × √7 = √ 14 which is an irrational number.
√5 × √5 = √ 25 = 5 which is a rational number.
Therefore Option A is not always true as the product of two irrational number can given both irrational and rational numbers.
b) the product of two rational numbers rational
Option b is always true and this is correct. For example
5× 5 = 25 which is a rational number
5/6 × 1/2 = 5/12 which is a rational number.
c) the sum of two rational numbers is irrational.
Option c is a wrong or false option and statement. This is because the sum of two rational numbers would always give you a rational number and not an irrational number.
For example: 5+ 4 = 9 (rational number)
2/5 + 1/5 =3/5 ( rational number)
Hence option c is a wrong option
d) the sum of an irrational number and a rational number is rational
Option d is an incorrect option and statement.
This is because, the sum of an irrational number and a rational number gives us an irrational number.
For example: 2(rational number ) + √2 (Irrational number) = 3.4142135624(Irrational number)
From the above explanation , we can see and observe that the only correct option and statement that is ALWAYS true is :
Option b) "the product of two rational numbers rational"
