Question

PLEASE HELP!!! Which expressions simplify to a rational answer? Select each correct answer.

Answer 1

ANSWER

The first three expressions will simplify to a rational answer.

EXPLANATION

Let us simplify the expressions then we can see which of them are rational.

A.

$7\sqrt{3} \times \sqrt{3}$

We multiply out the roots to get

$7\sqrt{3} \times \sqrt{3}=7 \times (\sqrt{3})^2$

This simplifies to

$7\sqrt{3} \times \sqrt{3}=7 \times 3$

$7\sqrt{3} \times \sqrt{3}=21$

This is a rational number hence the answer is rational.

B.

$\sqrt{5} \times \sqrt{5}=(\sqrt{5})^2$

$\sqrt{5} \times \sqrt{5}=5$

This is also a rational solution.

C.

$2\sqrt{9} \times \sqrt{4}=2\times3\times2$

$2\sqrt{9} \times \sqrt{4}=12$

This one too is a rational solution.

D.

$\sqrt{3} \times \sqrt{16}=\sqrt{3}\times4$

$\sqrt{3} \times \sqrt{16}=4\sqrt{3}$

This is an irrational answer because √3 is an irrational number and multiplying a rational number, 4 by an irrational number results in an irrational number.