**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√(x^{2}) +6√(y^{2}) – 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**