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प्रश्न
Show the number √7 on the number line.
उत्तर
Draw a number line as shown in the figure and mark the points O, A and B on it such that OA = AB = 1 unit. The point O represents 0 and B represents 2. At B, draw CB perpendicular on the number line such that BC = 1 unit. Join OC. Now, ∆OBC is a right angled triangle.
In ∆OBC, by Pythagoras theorem
(OC)2 = (OB)2 + (BC)2
= (2)2 + (1)2
= 4 + 1
= 5
∴ OC = √5
Taking O as centre and radius OC = √5 , draw an arc cutting the number line at D.
Clearly, OC = OD = √5
At D, draw ED perpendicular on the number line such that ED = 1 unit. Join OE. Now, ∆ODE is a right angled triangle.
In ∆ODE, by Pythagoras theorem
(OE)2 = (OD)2 + (DE)2
= (√5)2 + (1)2
= 5 + 1
= 6
∴ OE = √6
Taking O as centre and radius OE = √6 , draw an arc cutting the number line at F.
Clearly, OE = OF = √6
At F, draw GF perpendicular on the number line such that GF = 1 unit. Join OG. Now, ∆OFG is a right angled triangle.
In ∆OFG, by Pythagoras theorem
(OG)2 = (OF)2 + (FG)2
= (√6)2 + (1)2
= 6 + 1
= 7
∴ OG = √7
Taking O as centre and radius OG = √7 , draw an arc cutting the number line at H.
Clearly, OG = OH = √7
Hence, H represents √7 on the number line.
संबंधित प्रश्न
Show the following numbers on a number line. Draw a separate number line for each example.
(1)`3/2 , 5/2 , -3/2`
(2)`7/5 , (-2)/5 , (-4)/5`
(3) `(-5)/8 , 11/8`
(4)`13/10 , (-17)/10`
Show the following numbers on a number line. Draw a separate number line for the example.
`13/10 , (-17)/10`
Evaluate:
`1/(-15) + 5/(-12)`
The points S, Y, N, C, R, A, T, I and O on the number line are such that CN = NY = YS and RA = AT = TI = IO. Find the rational numbers represented by the letters Y, N, A, T and I
Draw a number line and represent the following rational numbers on it
`(-8)/3`
`-3/4` is smaller than –2.
The rational number `(-8)/(-3)` lies neither to the right nor to the left of zero on the number line.
The rational numbers can be represented on the number line.
Write the following rational numbers in the descending order.
`8/7, (-9)/8, (-3)/2, 0, 2/5`
On a number line, `4/3` is to the ______ of zero (0).
