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Answer 1

Answer:

$1) \: \sqrt{7} + \sqrt{6}$

$2) \: \sqrt{5} - \sqrt{2}$

$3) \: \sqrt{7} + 2$

$4) \: \frac{ \sqrt{2} }{2}$

$5) \: 2 - \sqrt{3}$

$6) \: \sqrt{3} + \sqrt{2}$

$7) \: 8$

$8) \: 2$

$9) \: 5$

$10) \: 27$

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Answer 2

Step-by-step explanation:

1) Given number = 1/(√7-√6)

Rationalising factor of √7-√6 = √7+√6

On Rationalising the denominator then

=>[1/(√7-√6)]×[(√7+√6)/(√7+√6)]

=> (√7+√6)/(√7-√6)(√7+√6)

=> (√7+√6)/[(√7)²-(√6)²]

Since (a+b)(a-b) = a²-b²

=> (√7+√6)/(7-6)

=> (√7+√6)/1

=> √7+√6

2)Given number = 1/(√5+√2)

Rationalising factor of √5+√2 = √5-√2

On Rationalising the denominator then

=>[1/(√5+√2)]×[(√5-√2)/(√5-√2)]

=> (√5-√2)/(√5-√2)(√5+√2)

=> (√5-√2)/[(√5)²-(√2)²]

Since (a+b)(a-b) = a²-b²

=> (√5-√2)/(5-2)

=> (√5-√2)/3

3)Given number = 1/(√7-2)

Rationalising factor of √7-2 = √7+2

On Rationalising the denominator then

=>[1/(√7-2)]×[(√7+2)/(√7+2)]

=> (√7+2)/(√7+2)(√7-2)

=> (√7+2)/[(√7)²-(2)²]

Since (a+b)(a-b) = a²-b²

=> (√7+2)/(7-4)

=> (√7+2)/3

4)Given number = 1/√2

Rationalising factor of √2 = √2

=> (1/√2)×(√2/√2)

=> √2/(√2×√2)

=> √2/2

5)Given number = 1/(2+√3)

Rationalising factor of 2+√3= 2-√3

On Rationalising the denominator then

=>[1/(2+√3)]×[(2-√3)/(2-√3)]

=> (2-√3)/(2+√3)(2-√3)

=> (2-√3)/[(2)²-(√3)²]

Since (a+b)(a-b) = a²-b²

=> (2-√3)/(4-3)

=> (2-√3)/1

=> 2-√3

6)Given number = 1/(√3-√2)

Rationalising factor of √3-√2 = √3+√2

On Rationalising the denominator then

=>[1/(√3-√2)]×[(√3+√2)/(√3+√2)]

=> (√3+√2)/(√3-√2)(√3+√2)

=> (√3+√2)/[(√3)²-(√2)²]

Since (a+b)(a-b) = a²-b²

=> (√3+√2)/(3-2)

=> (√3+√2)/1

=> √3+√2

7)Given number = (64)½

=> (2×2×2×2×2×2)½

=> (2⁶)½

=> (2)⁶/²

=> 2³

=> 8

8) Given number = (32)⅕

=>(2×2×2×2×2)⅕

=> (2⁵)⅕

=> (2)⁵/⁵

=> 2¹

=> 2

9) Given number = (125)⅓

=> (5³)⅓

=> 5³/³

=>5

10) Given number = 9³/²

=> (3²)³/²

=> 3³

=> 3×3×3

=> 27

Answer :-

1.c

2.c

3.c

4.d

5.a

6.b

7.a

8.c

9.a

10.b

Used formulae:-

• (a+b)(a-b) = a²-b²

• The Rationalising factor of √a+√b is √a-√b

• The Rationalising factor of√a-√b is √a+√b