Previous exercise – Surds – Exercise 7.1 – Class X
Surds – Exercise 7.2
I. Simplify
- √3 x √7
- ∛4 x ∛5
- ∜4 x ∜6
- 2∛7 x 3∛4
- √18 x √27 x √128
II. Find the product of the following surds.
- √2 and ∛4
- ∛3 and ∜2
- ∛5 and √2
- √3 and ∜5
- √5 and ∛5
III. Simplify
- (3√2 + 2√3)(2√3 – 4√2)
- (√75 – √45)( √20 + √12)
- (3√x + 2√y)(3√y – 2√x)
- (6√a – 5√a)(6√a + 5√b)
- (6√2 – 7√3)(6√2 – 7√3)
- (3√27 + 5)(9√3 + 7)
Surds – Exercise 7.2 – Solutions:
I. Simplify
- √3 x √7
Solution:
√3 x √7 = √(3×7)
= √21
- ∛4 x ∛5
Solution:
∛4 x ∛5 = ∛(4×5)
= ∛20
- ∜4 x ∜6
Solution:
∜4 x ∜6 = ∜(6×4)
= ∜24
4.
5.
6.
7. 2∛7 x 3∛4
Solution:
2∛7 x 3∛4 = (2×3)∛(7×4)
= 6∛28
- √18 x √27 x √128
Solution:
√18 x √27 x √128 = √(9×2) x √(9×3) x √(2×64)
= 3√2 x 3√3 x 8√2
= (3×8)√2 x 3√3
= 24√2 x 3√3
II. Find the product of the following surds.
- √2 and ∛4
Solution:
- ∛3 and ∜2
Solution:
- ∛5 and √2
Solution:
- √3 and ∜5
Solution:
- √5 and ∛3
Solution:
6.
7. ∛5 and ∜4
Solution:
III. Simplify
- (3√2 + 2√3)(2√3 – 4√2)
Solution:
(3√2 + 2√3)(2√3 – 4√2)
= 3√2(2√3 – 4√2) + 2√3(2√3 – 4√2)
= 6√6 – 12√4 + 4√9 – 8√6
= 6√6 – 12×2 + 4×3 – 8√6
= 6√6 – 24 + 12 – 8√6
= 6√6 – 12 – 8√6
= (6 – 8) √6 – 12
= -2√6 – 12
= -2(√6 – 6)
- (√75 – √45)( √20 + √12)
Solution:
(√75 – √45)( √20 + √12)
= √75(√20 + √12) – √45(√20 + √12)
= √1500 + √900 – √900 – √540
= 4√15
- (3√x + 2√y)(3√y – 2√x)
Solution:
(3√x + 2√y)(3√y – 2√x)
= 3√x(3√y – 2√x) + 2√y(3√y – 2√x)
= 9√xy – 6√(x2) +6√(y2) – 4√(xy)
= 9√(xy) – 6x + 6y – 4√(xy)
=(9 – 4)√(xy) – 6x + 6y
= 5√(xy) – 6x + 6y
- (6√a – 5√b)(6√a + 5√b)
Solution:
(6√a – 5√b)(6√a + 5√b)
= 6√a(6√a + 5√b) – 5√b(6√a + 5√b)
= 36a + 30√(ab) – 30√(ab) – 25b
= 36a – 25b
- (6√2 – 7√3)(6√2 – 7√3)
Solution:
(6√2 – 7√3)(6√2 – 7√3)
= 6√2(6√2 – 7√3) – 7√3(6√2 – 7√3)
= 36×2 – 42√(2×3) – 42√(2×3) + 49×3
= 72 – 42√6 – 42√6 +147
= 219 – 84√6
- (3√27 + 5)(9√3 + 7)
Solution:
(3√27 + 5)(9√3 + 7)
= 3√27 (9√3 + 7)+ 5(9√3 + 7)
= 27√(27×3) + 21√27 + 45√3 + 35
= 27√81 + 21√27 + 45√3 + 35
= 27×9 + 21×3√3 + 45√3 + 35
= 243 + 63√3 + 45√3 + 35
= 278 + 108√3
Next exercise – Surds – Exercise 7.3 – Class X