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Question
Show the number √5 on the number line.
Solution
Draw a number line as shown in the figure. Let the point O represent 0 and point Q represent 2. Draw a perpendicular QR at Q on the number line such that QR = 1 unit. Join OR. Now, ∆OQR is a right angled triangle.
By Pythagoras theorem, we have
OR2 = OQ2 + QR2
= (2)2 + (1)2
= 4 + 1
= 5
∴ OR = √5
Taking O as the centre and radius OR = √5, draw an arc cutting the number line at C.
Clearly, OC = OR = √5
Hence, C represents √5 on the number line.
RELATED QUESTIONS
The number `sqrt2` is shown on a number line. Steps are given to show `sqrt3` on the number line using `sqrt2`. Fill in the boxes properly and complete the activity.
Activity :
- The point Q on the number line shows the number ______.
- A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.
- Right angled ∆ORQ is obtained by drawing seg OR.
`l ("OQ") = sqrt2` , `l("QR") = 1`
`therefore` by Pythagoras theorem,
`[l("OR")]^2 = [l("OQ")]^2 + [l("QR")]^2 `
= `square^2`+ `square^2` = `square` + `square`
= `square`
∴ l(OR) = `square`
Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number `sqrt3`.
Evaluate:
`5/9 + (-7)/6`
Evaluate:
`(-8)/9 + -5/12`
Evaluate:
`0 + (-2)/7`
Evaluate:
`5/(-11) + 0`
Draw a number line and mark
`3/4, 7/4, (-3)/4 and (-7)/4` on it.
Draw a number line and represent the following rational numbers on it
`(-17)/(-5)`
The rational numbers `(-12)/(-5)` and `(-7)/17` are on the opposite sides of zero on the number line.
Represent the following rational numbers on a number line:
`3/8, (-7)/3, 22/(-6)`
Find a rational number exactly halfway between:
`1/15` and `1/12`
