Q4 of 114 Page 35

Prove that is irrational.

Assume to be rational. So we can write it in the form of a/b where a and b are co - prime.

So , a/b =


And ∴ b/a = √3


Since b/a is rational but √3 is irrational.


By contradiction is irrational.


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More from this chapter

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2

Classify the following numbers as rational or irrational:

i. ii. 3.1416


iii. π iv.


v. 5.636363 … vi. 2.040040004 …


vii. 1.535335333 … viii. 3.121221222 …


ix.

3

Prove that each of the following numbers is irrational.

i. ii.


iii. iv.


v. vi.


vii. viii.


xi.

5

i. Give an example of two irrationals whose sum is rational.

ii. Give an example of two irrational whose product is rational.

 6

State whether the given statement is true or false.

i. The sum of two rationals is always rational.


ii. The product of two rationals is always rational.


iii. The sum of two irrationals is always an irrational.


iv. The product of two irrationals is always an irrational.


v. The sum of rational and an irrational is irrational.


vi. The product of a rational and an irrational is irrational.