Solve :- [√5/(√3 + √2)] - [3√3/(√2 + √3)] + [2√2/(√3 + √5)]
Answers
Answer:
\frac{4 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } + \frac{3 \sqrt{5} }{ \sqrt{10} - \sqrt{3} } + \frac{5 \sqrt{3} }{ \sqrt{6} + \sqrt{5} } \\
On rationalizing the denominator we get,
= \frac{4 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } \times \frac{ \sqrt{15} + 3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } + \frac{3 \sqrt{5} }{ \sqrt{10} - \sqrt{3} } \times \frac{ \sqrt{10} + \sqrt{3} }{ \sqrt{10} + \sqrt{3} } + \frac{5 \sqrt{3} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } \\ \\ = \frac{4 \sqrt{2} ( \sqrt{15} + 3 \sqrt{2} )}{ {( \sqrt{15}) }^{2} - {(3 \sqrt{2} )}^{2} } + \frac{3 \sqrt{5}( \sqrt{10} + \sqrt{3} )}{ {( \sqrt{10}) }^{2} - {( \sqrt{3} )}^{2} } + \frac{5 \sqrt{3} ( \sqrt{6} - \sqrt{5}) }{ {( \sqrt{6}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ = \frac{4 \sqrt{30} + 24 }{15 - 18} + \frac{3 \sqrt{50} + 3 \sqrt{15} }{10 - 3} + \frac{5 \sqrt{18} - 5 \sqrt{15} }{6 - 5} \\ \\ = \frac{4 \sqrt{30} + 24}{ - 3} + \frac{3 \sqrt{2 \times 5 \times 5} + 3 \sqrt{15} }{7} + 5 \sqrt{3 \times 3 \times 2} - 5 \sqrt{15} \\ \\ = \frac{ - 4 \sqrt{30} - 24}{3} + \frac{15 \sqrt{2} + 3 \sqrt{15} }{7} + 15 \sqrt{2} - 5 \sqrt{15} \\ \\ = \frac{ - 4 \sqrt{30} \times 7 - 24 \times 7 + 15 \sqrt{2} \times 3 + 3 \sqrt{15} \times 3 + 15 \sqrt{2} \times 21 - 5 \sqrt{15} \times 21}{21} \\ \\ = \frac{ - 28 \sqrt{30} - 168 + 45 \sqrt{2} + 9 \sqrt{15} + 315 \sqrt{2} - 105 \sqrt{15} }{21} \\ \\ = \frac{ - 28 \sqrt{30} - 168 + 360 \sqrt{2} - 96 \sqrt{15} }{21}
Step-by-step explanation:
Answer:
=(√5-3√3/√2+√3)+(2√2/√3+√5)
=(2.2-1.7*3/1.4+1.7) +(2*1.4/1.3+2.2)
=(2.2-15.1/3.1) +(2.8/3.5)
=(-12.9/3.1) +(2.8/3.5)
=(-14.15+8.68/10.85)
=-36.47/10.85
=-3.36129
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