Question

Which expressions simplify to a rational answer? Select each correct answer. 29√⋅4√ 3√⋅16−−√ 73⋅−√3√ 5√⋅5√

Answer 1

2√9 × √4

√5 × √5

7√3 ×√3

Explanation:

Answer 2

The correct options are 1, 3 and 4.

Explanation:

We need to find the expressions whose simplified form is a rational number.

Rational number: If a number is defined in the form of p/q where p and q are integers and q≠0, then it is called a rational number.

For example: 0,2, 4.3 etc.

Irrational number: If a number can not defined in the form of p/q, where p and q are integers and q≠0, then it is called an irrational number.

First expression is

`2√(9)\cdot √(4)=2(3)\cdot (2)\Rightarrow 6\cdot 2=12`

12 is a rational number.

Second expression is

`√(3)\cdot √(16)=√(3)\cdot 4\Rightarrow 4√(3)`

`4√(3)` is an irrational number.

Third expression is

`7√(3)\cdot √(3)\Rightarrow 7\cdot 3=21`

21 is a rational number.

Fourth expression is

`√(5)\cdot √(5)=5`

5 is a rational number.

Therefore, the correct options are 1, 3 and 4.