Class IX Math NCERT Solutions For Real Numbers Exercise– 1.5

Exercise– 1.5
1.  Classify the following numbers as rational or irrational:
       
Ans.
       (i)   
              Since it is a difference of a rational and irrational number,
               is an irrational number.
       (ii)   
              We have:
              
              which is a rational number.
       (iii)   
              Since, 
               is a rational number.
       (iv)   
              ⇒ The quotient of rational and irrational is an irrational number.
               is an irrational number.
       (v)   2π
              ⇒ 2π = 2 × π = Product of a rational and an irrational (which is an irrational number)
              ⇒ 2π is an irrational number.
2.  Simplify each of the following expressions:
       
Ans.
       
3.  Recall,π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is,  This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Ans.
              When we measure the length of a line with a scale or with any other device, we only get an approximate rational value, i.e. c and d both are irrational.
              is irrational and hence π is irrational.
              Thus, there is no contradiction in saying that π is irrational.
4.  Rationalise the denominators of the following:
       
       
Ans.
       
       

Comments

Post a Comment

Popular posts from this blog

Class IX Math NCERT Solution for Circles 10.5

Image
EXERCISE 10.5 (Page 184) Q1.   In the figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOS = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC. Sol:  We have a circle with centre O, such that ∠AOB 60° and ∠BOC = 30°           ∵ ∠AOB + ∠BOC = ∠AOC           ∴ ∠AOC = 60° + 30° = 90°           Now, the arc ABC subtends ∠AOC = 90° at the centre and ∠ADC at a point D on the circle other than the arc ABC.            Q2.   A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. Sol:  We have a circle having a chord AB equal to radius of the circle.      ...
Read more

Class IX Math NCERT Solution for Heron’s Formula 12.2

Image
Exercise 12.2 (Page 206) . 1.    A park, in the shape of a quadrilateral ABCD, has �C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy? Ans.  Let us join B and D, such that BCD is a right–angled triangle.        We have area of BCD                 Now, to find the area of ABD, we need the length of BD.        ∴ In right, BCD,        BD 2  = BC 2  = CD 2 [Pythagoras theorem]        ⇒ BD 2  = 12 2  + 5 2        ⇒ BD 2  = 144 + 25 = 169 = 13 2                 2.    Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 ...
Read more

Class IX Math NCERT Solution for Surface Areas and Volumes 13.5

Image
EXERCISE 13.5 (Page 228) Q1.    A matchbox measures 4 cm × 2.5 cm. × 1.5 cm. What will be the volume of a packet containing 12 such boxes? Sol:  Measures of matchbox (cuboid) is 4 cm × 2.5 cm × 1.5 cm            ⇒ l = 4 cm, b = 2.5 cm and h = 1.5 cm            ∴ Volume of matchbox = (l × b) × h            = [4 cm × 2.5 cm] × 1.5 cm 3                        = 15 cm 3            ⇒ Volume of 12 boxes = 12 × 15 cm 3  = 180 cm 3 Q2.    A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?            (l m ...
Read more