Question

Please help I’m timed!!

Which expression represents a rational number?


5/9 + (square root of 18)

Pie+ (square root of 16)

2/7 + (square root of 121)

3/10 + (square root of 11)

Answer 1

5/9, 2/7, 3/10 are all rational numbers

Explanation:

Remember that all rational numbers are able to be written as a fraction or ratio of two integers.

Answer 2

`(2)/(7)+√(121)`

Explanation:

Since, a real number is called rational number if it can be expressed in the form of
`(p)/(q)`,

Where, p and q are integers,

S.t. q ≠ 0,

If the number is not a rational number then it is irrational,

Now, the sum or difference of two rational numbers is a rational number,

While, the sum or difference of a rational number and an irrational number is an irrational number.

∵ √18, √11 and
`\pi` are irrational numbers,

Also,
`(5)/(9)`,
`√(16)` and
`(3)/(10)` are rational number,

`\implies (5)/(9)+√(18),\pi+√(16), (3)/(10)+√(11)\text{ are irrational numbers}`

Now,

`(2)/(7)\text{ and }√(121)\text{ are rational numbers}`

Hence,

`(2)/(7)+√(121)\text{ is rational number}`