Question

Simplify Simplify Simplify​

Answer 1

Step-by-step explanation:

1) 2√50 + 3√32 + 4√18

= 2√ 25×2 + 3√16×2 + 4√9×2

= 2×5√2 + 3×4√2 + 4×3√2

= 10√2 + 12√2 + 12√2

= √2( 10+12+12). [ √2 is common to all]

= 34√2

Answer 2

Step-by-step explanation:

$(i) \: \: \: 2 \sqrt{50} + 3 \sqrt{32} + 4 \sqrt{18} \\ = 2 \sqrt{25 \times 2} + 3 \sqrt{16 \times 2} + 4 \sqrt{9 \times 2} \\ = 2 \sqrt{ {5}^{2} \times 2 } + 3 \sqrt{ {4}^{2} \times 2} + 4 \sqrt{ {3}^{2} \times 2} \\ = (2 \times 5) \sqrt{2} + (3 \times 4) \sqrt{2} + (4 \times 3) \sqrt{2} \\ = 10 \sqrt{2} + 12 \sqrt{2} + 12 \sqrt{2} \\ = (10 + 12 + 12) \sqrt{2} \\ = \underline{ \underline{ 34 \sqrt{2} }} \\ \\ (ii) \: \: \: \sqrt[4]{16} - 6 \sqrt[3]{343} + 18 \times \sqrt[5]{243} - \sqrt{196} \\ = \sqrt[4]{16} - (6 \sqrt[3]{343} ) + (18 \times \sqrt[5]{243}) - \sqrt{196} \\ = \sqrt[4]{{2}^{4}} - (6 \times \sqrt[3]{{7}^{3}} ) + (18 \times \sqrt[5]{{3}^{5}}) - \sqrt{{14}^{2}} \\ = 2 - (6 \times 7) + (18 \times 3) - 14 \\ = 2 - 42 + 54 - 14 \\ = \underline{ \underline{ 0}} \\ \\ (iii) \: \: \: \sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225} \\ = \sqrt[4]{{3}^{4}} - 8 \sqrt[3]{{6}^{3}} + 15 \sqrt[5]{{2}^{5}} + \sqrt{{15}^{2}} \\ = 3 - (8 \times 6) + (15 \times 2) + 15 \\ = 3 - 48 + 30 + 15 \\ = \underline{ \underline{ 0}}$