Question 2:

Simplify each of the following expressions:

(i) (3 + √3) (2+√2)        (ii) (3+√3) (3−√3)

(iii) (√5 +√2)²                    (iv) (√5−√2) (√5+√2)

Answer:

(i) (3+√3) (2+√2) = 3(2+√2) +√3(2+√2)

=6+3√2 + 2√3 + √6

(ii) (3+√3)(3−√3)=(3)² – (√3)²

= 9 – 3 =6

(iii) (√5+√2)² = (√5)² + (√2)² + 2(√5) (√2)

=5+2+2√10 = 7+2√10

(iv) (√5 – √2) (√5+√2) =(√5)² – (√2)²

5 – 2 = 3 

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