Question

If √2 = 1.414, √3 = 1.732, then find the value of 4/3√3−2√2 + 3/3√3+2√2.

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Answer 1

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$= > \bf \: \frac{4}{3 \sqrt{3} - 2 \sqrt{2} } + \frac{3}{3 \sqrt{3} + 2 \sqrt{2} } \\ \\ = \frac{4 (3\sqrt{3} + 2 \sqrt{2}) + 3(3 \sqrt{3} - 2 \sqrt{2}) }{(3 \sqrt{3} - 2 \sqrt{2} )( 3 \sqrt{3} + 2 \sqrt{2} ) } \\ \\ = \frac{12 \sqrt{3} + 8 \sqrt{2} + 9 \sqrt{3} - 6 \sqrt{2} }{ {(3 \sqrt{3} )}^{2} - {(2 \sqrt{2}) }^{2} } \\ \\ = \frac{21 \sqrt{3} + 2 \sqrt{2} }{27 - 8} = \frac{21 \sqrt{3} }{19} + \frac{2 \sqrt{2} }{19} \\ \\ = \frac{21 \times 1 .732}{19} + \frac{2 \times 1.414}{19} \\ \\ = 1.914 + 0.148 = \bf \underline{\: 2.06}$
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