[tex]\sqrt{5}[/tex] gives an irrational product when multuply it by [tex]0.2[/tex].
What is irrational number?
" Irrational number is defined as the set of numbers which can not be represented in [tex]\frac{x}{y} , y\neq 0[/tex] form."
According to the question,
Given multiplier [tex]= 0.2[/tex]
A. [tex]0.7[/tex]
The product of [tex]0.7 \times 0.2 = 0.14[/tex] which is not a irrational number but a decimal number.
Option A is not the correct answer.
B. [tex]5[/tex]
The product of [tex]5 \times 0.2 = 1[/tex] which is not a irrational number but a whole number.
Option B is not the correct answer.
C. [tex]\sqrt{5}[/tex]
The product of
[tex]\sqrt{5} \times 0.2 \\\\= \frac{2}{10}\times \sqrt{5} \\\\= \frac{1}{5} \times \sqrt{5}\\\\=\frac{1}{\sqrt{5} }[/tex]
which is a irrational number .
Option C is the correct answer.
D. [tex]\frac{3}{4}[/tex]
The product of
[tex]\frac{3}{4} \times 0.2\\\\= \frac{3}{4} \times\frac{2}{10}\\ \\=\frac{3}{20}[/tex]
which is not a irrational number but a fraction.
Hence, Option C is the correct answer.
Learn more about irrational number here
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