Question
Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$\sqrt{\Big(\frac{9}{27}\Big)}$
$\sqrt{\Big(\frac{9}{27}\Big)}$
✓
Answer
We have,
$\sqrt{\Big(\frac{9}{27}\Big)}$
$=\frac{3}{\sqrt{27}}$
$=\frac{1}{\sqrt{3}}$
Quotient of a rational and an irrational number is irrational numbers so $\frac{1}{\sqrt{3}}$ is an irrational number.
$\sqrt{\Big(\frac{9}{27}\Big)}$ is an irrational number.
$\sqrt{\Big(\frac{9}{27}\Big)}$
$=\frac{3}{\sqrt{27}}$
$=\frac{1}{\sqrt{3}}$
Quotient of a rational and an irrational number is irrational numbers so $\frac{1}{\sqrt{3}}$ is an irrational number.
$\sqrt{\Big(\frac{9}{27}\Big)}$ is an irrational number.
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