Question

Represent $\sqrt{5}$ on a number line with a given length of $\sqrt{2}$ and $\sqrt{3}.$
Consider the following steps and arrange them in a proper sequence.

(a)	Connect the other endpoints of both the lines to draw the hypotenuse.
(b)	Draw a perpendicular line of length $\sqrt{3}$ on the number line from the right end of the line of length $\sqrt{2}.$
(c)	Measure the length of the hypotenuse using a compass and mark it on the number line to represent $\sqrt{5}.$
(d)	Draw a line of length $\sqrt{2}$ on a number line with its left end on 0.

• A. $a\to b\to c\to d$
• B. $d\to b\to a\to c$
• C. $a\to b\to d\to c$

Answer 1

The correct option is B $d\to b\to a\to c$

From pythagoras theorem, ${\text{hypotenuse}}^2={\text{base}}^2+{\text{perpendicular}}^2$
$\Rightarrow (\sqrt{2}{)}^2+(\sqrt{3}{)}^2=2+3=5=(\sqrt{5}{)}^2$

To represent $\sqrt{5}$ on a number line, we perform the following steps:

1. Draw a line of length $\sqrt{2}$ on a number line with its left end on 0.
2. Draw a perpendicular line of length $\sqrt{3}$ on the number line from the right end of the line of length $\sqrt{2}.$
3. Connect the other endpoints of both the lines to draw the hypotenuse.
4. Measure the length of the hypotenuse using a compass and mark it on the number line to represent $\sqrt{5}.$