Q4 of 30 Page 24

The ratio of circumference to the diameter of a circle is represented by p. But we say that π is an irrational number. Why?

When we measure the length with a scale, we only get an approximate rational value, so we may not realize that in c and d which one is irrational.


So, either c or d is irrational and hence c/d is irrational i.e. π is irrational.


∴ π is an irrational number.


More from this chapter

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2

Classify the following numbers as rational or irrational.

i.


ii.


iii.


iv.


v. 2π


vi.


vii.

3

In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers.

i. x2 = 7 ii. y2 = 16


iii. z2 = 0.02 iv.


v. w2 = 27 vi. t4 = 256

 5

Rationalise the denominators of the following:

i.
ii.

iii.
iv. 6

Simplify each of the following by rationalising the denominator:

i. ii.


iii. iv.