**Question 1: Simplify each of the following:**

**Solution:**

(i)Using the formula:

Here,

(ii)Using the formula:

Here,

**Question 2: Simplify the following expressions:**

**(i) (4 + √7) (3 + √2)**

**(ii) (3 + √3)(5- √2 )**

**(iii) (√5 -2)( √3 – √5)**

**Solution:**

(i) (4 + √7) (3 + √2)= 12 + 4√2 + 3√7 + √14

(ii) (3 + √3)(5- √2)= 15 – 3√2 + 5√3 – √6

(iii) (√5 – 2)(√3 – √5)= √15 – √25 – 2√3 + 2√5

= √15 – 5 – 2√3 + 2√5

**Question 3: Simplify the following expressions:**

**(i) (11 + √11) (11 – √11)**

**(ii) (5 + √7) (5 –√7)**

**(iii) (√8 – √2 ) (√8 + √2)**

**(iv) (3 + √3) (3 – √3)**

**(v) (√5 – √2) (√5 + √2)**

**Solution:**

Using Identity: (a – b)(a + b) = a

^{2}– b^{2}

(i) (11 + √11) (11 – √11)= 11

^{2}– (√11)^{2}= 121 – 11

= 110

(ii) (5 + √7) (5 –√7)= (5

^{2}– (√7)^{2})= 25 – 7 = 18

(iii) (√8 – √2) (√8 + √2)= (√8)

^{2}– (√2)^{2}= 8 – 2

= 6

(iv) (3 + √3) (3 – √3)= (3)

^{2}– (√3)^{2}= 9 – 3

= 6

(v) (√5 – √2) (√5 + √2)= (√5)

^{2}– (√2)^{2}= 5 – 2

= 3

**Question 4: Simplify the following expressions:**

**(i) (√3 + √7)**^{2}

**(ii) (√5 – √3)**^{2}

**(iii) (2√5 + 3√2 )**^{2}

**Solution:**

Using identities: (a – b)

^{2}= a^{2}+ b^{2}– 2ab and (a + b)^{2}= a^{2}+ b^{2}+ 2ab

(i) (√3 + √7)^{2}= (√3)

^{2}+ (√7)^{2}+ 2(√3)(√7)= 3 + 7 + 2√21

= 10 + 2√21

(ii) (√5 – √3)^{2}= (√5)

^{2}+ (√3)^{2}– 2(√5)(√3)= 5 + 3 – 2√15

= 8 – 2√15

(iii) (2√5 + 3√2)^{2}= (2√5)

^{2}+ (3√2)^{2}+ 2(2√5)( 3√2)= 20 + 18 + 12√10

= 38 + 12√10