Chapter ISG, Problem 1.8STP

To determine

To select rational or irrational for each row

Answer to Problem 1.8STP

The product of $\sqrt{2}$ and $\sqrt{7}$ is irrational

The product of $\sqrt{2}$ and $\sqrt{18}$ is rational

The sum of $\pi$ and 19 is irrational

The sum of $\sqrt{17}$ and $\frac{3}{5}$ is irrational

The sum of $\sqrt{16}$ and 0.9 is rational

Explanation of Solution

Given information:

Product or sum	Rational	Irrational	Explanation
The product of $\sqrt{2}$ and $\sqrt{7}$
The product of $\sqrt{2}$ and $\sqrt{18}$
The sum of $\pi$ and 19
The sum of $\sqrt{17}$ and $\frac{3}{5}$
The sum of $\sqrt{16}$ and 0.9

Calculation:

The product of $\sqrt{2}$ and $\sqrt{7}$

Solving,

= $\sqrt{2}\times \sqrt{7}$

So,

= $\sqrt{14}$

  $\sqrt{14}$ is not a rational number because it cannot be written in fractions after square rooting.

The product of $\sqrt{2}$ and $\sqrt{18}$

Solving,

= $\sqrt{2}\times \sqrt{18}$

So,

= $\sqrt{36}$

Square rooting, 6 is the result. It is rational.

Sum of $\pi$ and 19

Solving,

  $\pi +19$

We know that $\pi$ is irrational, so any number added to it is also irrational. Hence, it is irrational.

Sum of $\sqrt{17}$ and $\frac{3}{5}$

Solving,

= $\sqrt{17}+\frac{3}{5}$

  $\sqrt{17}$ is irrational so any number added to it is also irrational. Hence, it is irrational.

Sum of $\sqrt{16}$ and 0.9

Solving,

= $\sqrt{16}+0.9$

So,

=4+0.9

Hence, 4.9 is rational as it can be can be expressed in fraction