Question

Which of the foolowing steps are required to represent $\sqrt{10}$ on a number line.

• A. Draw a line of length 3 units from 0 in right direction on a number line.
• B. Draw a perpendicular line of length 1 unit from right end of the line of length 3 units.
• C. Draw a horizontal line of length 1 unit from right end of the line of length 3 units.
• D. Connect the other end points of both lines to draw the hypotenuse.
• E. Measure the length of the hypotenuse using a compass and mark it on the number line to represent $\sqrt{10}.$

Answer 1

Answer: (A), (B), (D), (E)

Measure the length of the hypotenuse using a compass and mark it on the number line to represent $\sqrt{10}.$

From pythagorean theorem, ${\text{hypotenuse}}^2={\text{base}}^2+{\text{perpendicular}}^2$
$\Rightarrow (\sqrt{10}{)}^2=10=9+1=(3{)}^2+(1{)}^2$

To represent $\sqrt{10}$ on a number line, we perform the following steps:

1. Draw a line of length 3 units on a number line from 0 in its right direction.
2. Draw a perpendicular line of length 1 unit on the number line from the right end of the first line.
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 $\sqrt{10}.$