Exercise 1.4
1. Classify the following numbers as rational or irrational.
(i)
(ii)
(iii)(
(iv)2π :
(v)
2. Simplify each of the following expressions:
(i) (3 +
- We use distributive property.
- Applying: (a + b) (c + d) = ac + ad + bc + bd
- (3 +
3 2 + 3 2 3 + 3 2 - =
+ 2 3 6 - We have found the answer.
(ii)
- We use identity property.
- Applying: (a + b)(a - b) =
a 2 − b 2 3 + 3 3 − 3 - - =
- = - We have found the answer.
(iii)
- We use identity property.
- Applying:
a + b 2 a 2 b 2 - We get:
5 + 2 2 5 2 2 × 5 × 2 2 2 - =
+ 2 10 - =
+ 2 10 - We have found the answer.
(iv)
- We use identity property.
- Applying:
a + b 2 a 2 b 2 - We get: (
5 − 2 5 + 2 - - =
- = - We have found the answer.
3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π =
π is defined as the ratio of the circumference of a circle to its diameter, that is, π = c/d. Hence, we see that π is a
But, we know that π is an irrational number. In fact, the value of π is calculated as the
In conclusion, π is an
4. Represent
Let AB be of a length '9.3' units on the numberline.
Now, extend AB upto a point C on the numberline such that BC is 1 unit.
Taking AC of length
Using D as the center, draw a semi-circle/circle and also extend AC further, to see where this circle intersects the numberline.
From point B, draw a perpendicular intersecting the circle. Join BE. Now, project it onto the numberline.
The length of the segment BE is equal to
5. Rationalise the denominators of the following:
(i)
(ii)
(iii)
(iv)