Question2: Simplify each of the following expressions:

-Ushma Gaur, Subject Matter Expert at Edumarz

(i) (3 + √3)(2 + √2)

Solution: (3 + √3)(2 + √2) = 6 + 3√2 + 2√3 + √3√2

                                           = 6 + 3√2 + 2√3 + √6

(ii) (3 + √3)(3 − √3)

Solution: (3 + √3)(3 − √3) = 9 − 3√3 + 3√3 − √3√3

                                           = 9 − √3√3

                                           = 9 − 3

                                           = 6

(iii) (√5 + √2)^2

Solution: (√5 + √2)^2 = (√5 + √2)(√5 + √2)

                                    = √5√5 + √5√2 + √2√5 + √2√2

                                    = 5 + √10 + √10 + 2

                                    = 7 + 2√10

(iv) (√5 − √2)(√5 + √2)

Solution: (√5 − √2)(√5 + √2) = √5√5 + √5√2 − √2√5 − √2√2

                                              = 5 − 2

                                              = 3