Rationalize the denominator of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732, upto three places of decimal:
(i) √2/(2 + √2)
(ii) 1/(√3 + √2)
Solution:
(i) √2/(2 + √2)
By rationalizing the denominator,
√2/(2 + √2) = [√2(2 – √2)] / [(2 + √2) (2 – √2)]
= [2√2 – 2] / [22 – (√2)2]
= [2√2 – 2] / [4 – 2]
= 2[√2 – 1] / 2
= √2 – 1
= 1.414 – 1
= 0.414
(ii) 1/(√3 + √2)
By rationalizing the denominator,
1/(√3 + √2) = [1(√3 – √2)] / [(√3 + √2) (√3 – √2)]
= [(√3 – √2)] / [(√3)2 – (√2)2]
= [(√3 – √2)] / [3 – 2]
= [(√3 – √2)] / 1
= (√3 – √2)
= 1.732 – 1.414
= 0.318
More Solution:
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