Question

Which expression below equal a rational number ? Choose all that apply

Answer 1

ANSWER

The rational numbers are;

B.

`7 √(5) - √(245)`

C.


`(4)/(5) + (3)/(8)`

D.


`(4 √(7) )(2 √(7) )`

Step-by-step explanation

The first expression is


`\pi * √(36)`

When we simplify this obtain,


`= \pi * 6 = 6\pi`

Since π is an irrational number, all its multiples are also irrational.

The second expression is


`7 √(5) - √(245)`


`7 √(5) - √(49 * 5)`

We simplify to obtain,


`7 √(5) - √(49) * √(5)`


`= 7 √(5) - 7√(5) = 0`

This is a rational number, because

`0 = (0)/(1)`

The third expression is


`(4)/(5) + (3)/(8)`


`= (8 * 4 + 3 * 5)/(40)`


`= (32 + 15)/(40)`


`= (47)/(40)`

This is also a rational number.

The fourth expression is


`(4 √(7) ) * (2 √(7) ) = 4 * 2 * √(7) * √(7)`


`= 8 * ({ √(7) })^(2)`


`= 8 * 7 = 56`

This is also a rational number.

The last option is


`√(100) + √(5) = 10 + √(5)`

The sum of a rational number 10 and an irrational number √5 is an irrational number.