Question

number system exercise-1.5

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)



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Answer 1

Answer:

i 6+√6+2√3+3√2

ii 6

iii 7+2+√7

iv3

Answer 2

Answer:

Step-by-step explanation:

$i) (3 + \sqrt{3})(2 + \sqrt{2})\\=3(2 + \sqrt{2}) + \sqrt{3}(2 + \sqrt{2})\\= 6 +3\sqrt{2} + 2\sqrt{3} + \sqrt{6}\\\\ii)(3 + \sqrt{3})(3-\sqrt{3})\\=(3)^2 -(\sqrt{3})^2\\=9-3=6\\\\iii) (\sqrt{5} +\sqrt{2})^2\\=(\sqrt{5})^2 + 2(\sqrt{5})(\sqrt{2}) +(\sqrt{2})^2\\=5+2\sqrt{10}+2\\=7 +2\sqrt{10}\\\\iv)(\sqrt{5} - \sqrt{2})(\sqrt{5}+\sqrt{2})\\=(\sqrt{5})^2 -(\sqrt{2})^2\\=5-2=3$