Q. 54.3( 32 Votes )

# Rationalise the denominators of the following:

i.

ii.

iii.

iv.

Answer :

i.

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

By rationalizing,

⇒

__We know that (a + √b) (a - √b) = a ^{2} – 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.__

∴

Rate this question :

Classify the following numbers as rational or irrational.

i.

ii.

iii.

iv.

v. 2π

vi.

vii.

AP- MathematicsSimplify the following expressions.

i.

ii.

iii.

iv.

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

AP- MathematicsFind:

i. ii.

iii. iv.

v. vi.

AP- MathematicsFind five rational numbers between 1 and 2.

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