Question

An irrational number $\sqrt{n+1}$ can be represented on the number line by creating a right-angled triangle of sides:

• A. $1$ and $\sqrt{n+1}$
• B. $1$ and $n$
• C. $1$ and $n+1$
• D. $1$ and $\sqrt{n}$

Answer 1

The correct option is D $1$ and $\sqrt{n}$

Let $\sqrt{n+1}$ represents hypotenuse of right-angled triangle.

Let $x,y$ represents two sides of a right-angle triangle.

$x^2+y^2=(\sqrt{n+1}{)}^2$

$⟹x^2+y^2=n+1$ ......... (1)

If $x=1$ and $y=\sqrt{n+1}$ then (1) is not true.

If $x=1$ and $y=\sqrt{n+1}$ then (1) is not true.

If $x=1$ and $y=n+1$ then (1) is not true.

But, If $x=1$ and $y=\sqrt{n}$ then (1) is true.

Hence, other two sides are $1$ and $\sqrt{n}$.