Maths Rational and irrational Numbers Exercise1-4
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Q1 Simplify the following:
(i) √45 - 3√20 + 4√5
(ii) 3√3 + 2√27 + 7/√3
(iii) 6√5 × 2√5
(iv) 8√15 ÷ 2√3
(v) √24/8 + √54/9
(vi) 3/√8 + 1/√2
Q2 Simplify the following:
(i) (5 + √7) (2 + √5)
(ii) (5 + √5) (5 - √5)
(iii) (√5 + √2) 2>
(iv) (√3 - √7) 2>
(v) (√2 + √3) (√5 + √7)
(vi) (4 + √5) (√3 - √7)
Q3 If √2 = 1.414, then find the value of
(i) √8 + √50 + √72 + √98
(ii) 3√32 - 2√50 + 4√128 - 20√18
Q4 If √3 = 1.732, then find the value of
(i) √27 + √75 + √108 - √243
(ii) 5√12 - 3√48 + 6√75 + 7√108
Q5 State which of the following are rational or irrational decimals.
(i) √(4/9), -3/70, √(7/25), √(16/5)
(ii) -√(2/49), 3/200, √(25/3), -√(49/16)
Q6 State which of the following are rational or irrational decimals.
(i) -3√2
(ii) √(256/81)
(iii) √(27×16)
(iv) √(5/36)
Q7 State which of the following are irrational numbers.
(i) 3 - √(7/25)
(ii) -2/3 + ∛2
(iii) 3/√3
(iv) -2/7 ∛5
(v) (2 - √3) (2 + √3)
(vi) (3 + √5) 2
(vii) (2/5 √7) 2
(viii) (3 - √6) 2
Q8 Prove the following are irrational numbers.
(i) ∛2
(ii) ∛3
(iii) ∜5
Q9 Find the greatest and the smallest real numbers.
(i) 2√3, 3/√2, -√7, √15
(ii) -3√2, 9/√5, -4, 4/3 √5, 3/2√3
Q10 Write in ascending order.
(i) 3√2, 2√3, √15, 4
(ii) 3√2, 2√8, 4, √50, 4√3
Q11 Write in descending order.
(i) 9/√2, 3/2 √5, 4√3, 3√(6/5)
(ii) 5/√3, 7/3 √2, -√3, 3√5, 2√7
Q12 Arrange in ascending order.
∛2, √3, 6√5
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