Question

simplify a)4√12×7√6
b ) √24/8+√54/9
c)4√28÷3√7
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Answer 1

Answer:

a. (7√6)/12

b. 8/3

c. 168√2

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Answer 2

$a) \: 4 \sqrt{12} \times 7 \sqrt{6} \\ = 7 \times 4 \sqrt{12 \times 6} \\ = 28 \sqrt{2 \times 2 \times 3 \times 2 \times 3} \\ = 28 \times 2 \times 3 \sqrt{2} \\ \bf = 168 \sqrt{2}$

$b) \frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9} \\ \\ = \frac{ \sqrt{2 \times 2 \times 2 \times 3} }{8} + \frac{ \sqrt{2 \times 3 \times 3 \times 3} }{9} \\ \\ = \frac{2 \sqrt{6} }{8} + \frac{3 \sqrt{6} }{9} \\ \\ = \frac{2 \sqrt{6} \times 9 + 3 \sqrt{6} \times 8 }{72} \\ \\ = \frac{18 \sqrt{6} + 24 \sqrt{6} }{72} \\ \\ = \frac{42 \sqrt{6} }{72} \\ \\ \bf = \frac{7 \sqrt{6} }{12}$

$c) \frac{4 \sqrt{28} }{3 \sqrt{7} } \\ \\ = \frac{4 \sqrt{2 \times 2 \times 7} }{3 \sqrt{7} } \\ \\ = \frac{4 \times 2 \sqrt{7} }{3 \sqrt{7} } \\ \\ \bf = \frac{8}{3}$