Find the values of each of the following correct to three places of decimals, it being given that √2 = 1.414,√3 = 1.732, √5=2.236, √6= 2.4495 and √10= 3.162.
(i) 3 - √5 / 3 + 2√5 (ii) 1 + √2 / 3 -2√2
Answers
Given : √2 = 1.414,√3 = 1.732, √5 =2.236, √6 = 2.4495 and √10 = 3.162.
(i) We have 3 - √5 / 3 + 2√5
On putting the given values we get :
= (3 - 2.236) / (3 + 2 × 2.236)
= 0.764/ (3 + 4.472)
= 0.764/7.472
= 764/7472
= 0.102
3 - √5 / 3 + 2√5 = 0.102
Hence the value of 3 - √5 / 3 + 2√5 correct to three places of decimals is 0.102.
(ii) We have (1 + √2) / (3 -2√2)
On putting the given values we get :
= (1 + 1.414) / (3 - 2 × 1.414)
= 2.414/(3 - 2.828)
= 2.414/0.172
= 2414/172
(1 + √2) / (3 -2√2) = 14.035
Hence the value of (1 + √2) / (3 -2√2) correct to three places of decimals is 14.035.
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