Question

Show that 42-√3 is an irrationalnumber

Answer 1

Correct QuestioN :

Given : √3 is an Irrational number then, Show that 42 - √3 is an Irrational number.

To ProvE :

42-√3 is an irrational number

SolutioN :

Let assume 42 - √3 is a rational number.

• So, Condition for Rational number it can Express in the form of p / q .
• Where q ≠ 0.

→ 42 - √ 3 = p / q .

→ - √3 = p / q - 42

→ - √3 = p - 42q / q

$\rule{90}2$

Now, We are notice √3 is an Irrational number which can not Express in the form of p / q and p - 42q / q is a Rational number which can Express in the form of p / q.

✦ But, Irrational number ≠ Rational number.

So, We can say Our assumption was Wrong 42 - √3 is an Irrational number.

✡ Hence Proved.