Question:
If both a and b are rational numbers, find the values of a and b in each of the following equalities :
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer:
(i) Rationalising the denominator, we have
=>
=>
=>
=>
=>
and
[ on equating rational and irrational parts]
(ii) Multiplying the numerator and denominator by the rationlisation factor of the denominator, we get
=>
∴
=>
=>
=>
(iii) Multiplying the numerator and denominator by rationalisation factor of the denominator , we have
=>
=>
=>
=>
∴
=>
(iv)Multiplying the numerator and denominator by rationalisation factor of the denominator, we get
=>
=>
=>
∴
(v) Rationalising the denominator, we get
=>
=>
∴
(vi) Multiplying the numerator and denominator by rationalisation factor of the denominator, we get
=>
=>
=>
=>
∴
=>
Q 25.
Find the value to three places of decimals, of each of the following:
It is given that 2 = 1.414 , 3 = 1.732, 10 = 3.162 and 5 = 2.236 (approx.).
(i) 2 + 1 5 (ii) 2 - 3 3 (iii) 10 - 5 2