Q5 of 30 Page 24

Rationalise the denominators of the following:

i.
ii.

iii.
iv.

i.


Here, the conjugate of the denominator (3 + √2) is (3 - √2).


By rationalizing,


⇒


We know that (a + √b) (a - √b) = a2 – b.



∴


ii.


Here, the conjugate of the denominator (√7 - √6) is (√7 + √6).


By rationalizing,


⇒


We know that (√a + √b) (√a - √b) = a – b.



∴


iii.


By rationalizing the denominator,


⇒


∴


iv.


Here, the conjugate of the denominator (√3 - √2) is (√3 + √2).


By rationalizing,


⇒


We know that (√a + √b) (√a - √b) = a – b.






∴


More from this chapter

All 30 →
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

 4

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

 6

Simplify each of the following by rationalising the denominator:

i. ii.


iii. iv.

7

Find the value of upto three decimal places. (take √2 = 1.414 and √5 = 2.236)