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
(i) The rationalising factor of the denominator is , 2
∴ 2 + 1 5 = 2 + 1 5 × 5 5 = 2 + 1 × 5 5 2 = 2 × 5 + 5 5
=> 2 + 1 5 = 10 + 5 5 = 3.162 + 2.236 5 = 3.464 − 3 3 = 0.464 3 = 0.154
(ii) The rationalising factor of the monomial in the denominator is 3 .
∴ 2 - 3 3 = 2 - 3 3 × 3 3 = 2 - 3 3 3 2 = 2 3 - 3 2 3
=> 2 - 3 3 = 2 3 - 3 3 = 2 × 1.732 - 3 3 = 3.464 − 3 3 = 0.464 3 = 0.154
(iii)The rationalising factor of the denominator is 2 .
∴ 10 - 5 2 = 10 - 5 2 × 2 2 = 10 − 5 2 2
=> 10 - 5 2 = 10 × 5 − 10 × 5 2 2 = 10 × 2 − 5 × 2 2
=> 10 - 5 2 = 4 × 5 − 10 2 = 2 5 − 10 2
=> 10 - 5 2 = 2 × 2.236 − 3.162 2 = 4.472 − 3.162 2 = 1.310 2 = 0.655
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