Question

simplify 2√8/9-3√1/2+5√9/8​

Answer 1

$2 \sqrt{ \frac{8}{9} } - 3 \sqrt{ \frac{1}{2} } + 5 \sqrt{ \frac{9}{8} } \\ \\ = 2 \times 2 \frac{ \sqrt{2} }{3} - 3 \frac{1}{ \sqrt{2} } + 5 \times \frac{1}{2} \times \frac{3}{ \sqrt{2} } \\ \\ = \frac{4}{3} \sqrt{2} - \frac{3}{ \sqrt{2} } + \frac{15}{2 \sqrt{2} } \\ \\ = \frac{4 \sqrt{2} }{3} - \frac{3 \sqrt{2} }{2} + \frac{15 \sqrt{2} }{4} \\ \\ = \frac{16 \sqrt{2} - 18 \sqrt{2} + 45 \sqrt{2} }{12} \\ \\ = \frac{43 \sqrt{2} }{12}$

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