Math, asked by shreyanshmishra6, 10 months ago

Simplify each of the following expressions:

(i) (3 3 2 2 + + ) ( ) (ii) (3 3 3 3 + − ) ( )

(iii) ( )

2

5 2 + (iv) ( 5 2 5 2 − + ) ( )

3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter

(say d). That is, π =

c

d

⋅ This seems to contradict the fact that π is irrational. How will

you resolve this contradiction?​

Answers

Answered by amitnrw
1

Given : π is defined as the ratio of the circumference (say c) of a circle to its diameter.  Does it  contradict the fact that π is irrational

To find :  resolve this contradiction

Solution:

π is defined as the ratio of the circumference (say c) of a circle to its diameter

π  = Circumference of circle  / Diameter of circle

c = Circumference  of circle

d = Diameter of circle

=> π  = c/d

any number which can be written in the form of p/q

is rational number

where p , q  ∈ Z   and q ≠ 0

Hence  π  would be rational number if

c , d   ∈ Z   and d ≠ 0

but c & d both are not integer together

hence π is not rational

so  π is irrational

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