Question

how to represent √3 and √5​ on number line

Answer 1

Answer⤵

To draw √5 on number line

Steps involved are as follows:

Step I: Draw a number line and mark the center point as zero.

Step II: Mark right side of the zero as (1) and the left side as (-1).

Step III: We won’t be considering (-1) for our purpose.

Step IV: With 2 units as length draw a line from (1) such that it is perpendicular to the line.

Step V: Now join the point (0) and the end of the new line of 2 units length.

Step VI: A right-angled triangle is constructed.

Step VII: Now let us name the triangle as ABC such that AB is the height (perpendicular), BC is the base of triangle and AC is the hypotenuse of the right-angled ΔABC.

Step VIII: Now the length of the hypotenuse, i.e., AC can be found by applying Pythagoras theorem to the triangle ABC.

AC2 = AB2 + BC2

⟹ AC2 = 22 + 12

⟹ AC2 = 4 + 1

⟹ AC2 = 5

⟹ AC= √5

Step IX: Now with AC as radius and C as the center cut an arc on the same number line and name the point as D.

Step X: Since AC is the radius of the arc and hence, the CD will also be the radius of the arc whose length is √5.

Step XI: Hence, D is the representation of√5 on the number line.

Or

for √3 see the attachment

Hope it helps you frnd