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Question
Show the number √7 on the number line.
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Solution
To represent √7 on the number line, use the following construction:
- Draw a number line and mark the points O(0), A(2), and B(3).
- At point A, draw a perpendicular line AC of length √3 units.
- Join O to C. By the Pythagorean theorem,
`OC = sqrt(2^2 + (sqrt3)^2)`
`=sqrt(4+3)`
`=sqrt7` - With O as the centre and radius OC, draw an arc that cuts the number line at point P.
- The point P represents the number √7 on the number line.
Since √7 ≈ 2.646, it lies between 2 and 3 on the number line.
RELATED QUESTIONS
Represent these numbers on the number line.
`-5/6`
Show the following numbers on a number line. Draw a separate number line for the example.
`13/10 , (-17)/10`
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:
`0 + (-2)/7`
Evaluate:
`2 + (-3)/5`
Evaluate:
`4/(-9) + 1`
The rational number `57/23` lies to the left of zero on the number line.
Arrange the numbers `1/4, 13/16, 5/8` in the descending order.
Find a rational number exactly halfway between:
`1/6` and `1/9`
Find a rational number exactly halfway between:
`1/15` and `1/12`
