Question

i) √5 + √80
ii) √50 - √32
iii)√363 - √147
iv) 2√12 + √75 - 7√3
v) √7 × √14
vi) 8√12 × 3√24​

Answer 1

Step-by-step explanation:

$(i) \sqrt{5} + \sqrt{16 \times 5} \\ = \sqrt{5} + 4 \sqrt{5} \\ = 5 \sqrt{5}$

$(ii) \sqrt{50} - \sqrt{32} \\ = \sqrt{25 \times 2} - \sqrt{16 \times 2} \\ = 5 \sqrt{2} - 4\sqrt{2} \\ = 1 \sqrt{2}$

$(iii) \sqrt{363} - \sqrt{147} \\ = \sqrt{121 \times 3} - \sqrt{49 \times 3} \\ = 11 \sqrt{3} - 7 \sqrt{3} \\ = 4 \sqrt{3}$

$(iv)2 \sqrt{12} + \sqrt{75} - 7 \sqrt{3} \\ = 2 \sqrt{4 \times 3} + \sqrt{25 \times 3} - 7 \sqrt{3} \\ = 2 \times 2 \sqrt{3} + 5 \sqrt{3} - 7 \sqrt{3} \\ = 4 \sqrt{3} + 5 \sqrt{3} - 7 \sqrt{3} \\ = (4 + 5 - 7) \sqrt{3} \\ = 2 \sqrt{3}$

$(v) \sqrt{7} \times \sqrt{14} \\ = \sqrt{98} \\ = \sqrt{49 \times 2} \\ = 7 \sqrt{2}$

$(vi)8 \sqrt{12} \times 3 \sqrt{24} \\ = 8 \sqrt{4 \times 3} \times 3 \sqrt{4 \times 6} \\ = 16 \sqrt{3} \times 6 \sqrt{6} \\ = 96 \sqrt{18} \\ = 96 \sqrt{9 \times 2} \\ = 288 \sqrt{2}$