Question

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

Answer 1

Answer:

The correct options are 1, 3 and 4.

Step-by-step 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

$2\sqrt{9}\cdot \sqrt{4}=2(3)\cdot (2)\Rightarrow 6\cdot 2=12$

12 is a rational number.

Second expression is

$\sqrt{3}\cdot \sqrt{16}=\sqrt{3}\cdot 4\Rightarrow 4\sqrt{3}$

$4\sqrt{3}$ is an irrational number.

Third expression is

$7\sqrt{3}\cdot \sqrt{3}\Rightarrow 7\cdot 3=21$

21 is a rational number.

Fourth expression is

$\sqrt{5}\cdot \sqrt{5}=5$

5 is a rational number.

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