Surds – Exercise 7.2 – Class X

Previous exercise –  Surds – Exercise 7.1 – Class X

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Surds – Exercise 7.2

I. Simplify

1. √3 x √7
2. ∛4 x ∛5
3. ∜4 x ∜6
4. 
5. 2∛7 x 3∛4
6. √18 x √27 x √128

II. Find the product of the following surds.

1. √2 and ∛4
2. ∛3 and ∜2
3. ∛5 and √2
4. √3 and ∜5
5. √5 and ∛5
6. 

III. Simplify

1. (3√2 + 2√3)(2√3 – 4√2)
2. (√75 – √45)( √20 + √12)
3. (3√x + 2√y)(3√y – 2√x)
4. (6√a – 5√a)(6√a + 5√b)
5. (6√2 – 7√3)(6√2 – 7√3)
6. (3√27 + 5)(9√3 + 7)

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Surds – Exercise 7.2 – Solutions:

I. Simplify

1. √3 x √7

Solution:

√3 x √7 = √(3×7)

= √21

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2. ∛4 x ∛5

Solution:

∛4 x ∛5 = ∛(4×5)

= ∛20

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3. ∜4 x ∜6

Solution:

∜4 x ∜6 = ∜(6×4)

= ∜24

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4.

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5.

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6.

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7. 2∛7 x 3∛4

Solution:

2∛7 x 3∛4 = (2×3)∛(7×4)

= 6∛28

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8. √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

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II. Find the product of the following surds.

1. √2 and ∛4

Solution:

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2. ∛3 and ∜2

Solution:

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3. ∛5 and √2

Solution:

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4. √3 and ∜5

Solution:

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5. √5 and ∛3

Solution:

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6.

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7. ∛5 and ∜4

Solution:

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III. Simplify

1. (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)

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2. (√75 – √45)( √20 + √12)

Solution:

(√75 – √45)( √20 + √12)

= √75(√20 + √12) – √45(√20 + √12)

= √1500 + √900 – √900 – √540

= 4√15

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3. (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

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4. (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

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5. (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

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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

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Next exercise – Surds –  Exercise 7.3 – Class X

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