Maths Rational and irrational Numbers Exercise1-5
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Q1 Rationalize the denominator of the following:
(i) 3/4√5
(ii) 5√7 / √3
(iii) 3/(4 - √7)
(iv) 17/(3√2 + 1)
(v) 16/ (√41 - 5)
(vi) 1/ (√7 - √6)
(vii) 1/ (√5 + √2)
(viii) (√2 + √3) / (√2 - √3)
Q2 Simplify each of the following by rationalizing the denominator:
(i) (7 + 3√5) / (7 - 3√5)
(ii) (3 - 2√2) / (3 + 2√2)
(iii) (5 - 3√14) / (7 + 2√14)
Q3 Simplify:
[7√3 / (√10 + √3)] – [2√5 / (√6 + √5)] – [3√2 / (√15 + 3√2)]
Q4 Simplify:
[1/(√4 + √5)] + [1/(√5 + √6)] + [1/(√6 + √7)] + [1/(√7 + √8)] + [1/(√8 + √9)]
Q5 Give a and b are rational numbers. Find a and b if:
(i) [3 - √5] / [3 + 2√5] = -19/11 + a√5
(ii) [√2 + √3] / [3√2 - 2√3] = a - b√6
(iii) {[7 + √5]/[7 - √5]} – {[7 - √5]/[7 + √5]} = a + 7/11 b√5
Q6 If {[7 + 3√5] / [3 + √5]} – {[7 - 3√5] / [3 - √5]} = p + q√5, find the value of p and q where p and q are rational numbers.
Q7 Rationalise 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)
Q8 If a = 2 + √3, find 1/a, (a – 1/a)
Q9 Solve:
If x = 1 - √2, find 1/x, (x – 1/x)4
Q10 Solve:
If x = 5 - 2√6, find 1/x, (x2 – 1/x2 )
Q11 If p = (2-√5)/(2+√5) and q = (2+√5)/(2-√5), find the values of
(i) p + q
(ii) p – q
(iii) p2 + q2
(iv) p2 – q 2
Q12 If x = (√2 - 1)/( √2 + 1) and y = (√2 + 1)/( √2 - 1), find the value of x2 + 5xy + y2 .
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