Show that 7-3-10-3-2-5-6-5-3-2-15-3-2-1

L.H.S =7√(3)√(10)+√(3) 2√(5)√(6)+√(5) 3√(2)√(15)+3√(2) =7√(3)√(10)+√(3)×√(10) √(3)√(10) √(3) 2√(5)√(6)+√(5)×√(6) √(5)√(6) √(5) 3√(2)√(15)+3√(2)×√(15) 3 ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

Show that 7...

Question

Show that $\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}} = 1$

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Solution

L.H.S $= \frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}$

$= \frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} \times \frac{\sqrt{10} - \sqrt{3}}{\sqrt{10} - \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} \times \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} - \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}} \times \frac{\sqrt{15} - 3 \sqrt{2}}{\sqrt{15} - 3 \sqrt{2}}$

$= \frac{7 \sqrt{3} (\sqrt{10} - \sqrt{3})}{10 - 3} - \frac{2 \sqrt{5} (\sqrt{6} - \sqrt{5})}{6 - 5} - \frac{3 \sqrt{2} (\sqrt{15} - 3 \sqrt{2})}{15 - 18}$

$= \frac{7 \sqrt{3} (\sqrt{10} - \sqrt{3})}{7} - \frac{2 \sqrt{5} (\sqrt{6} - \sqrt{5})}{1} - \frac{3 \sqrt{2} (\sqrt{15} - 3 \sqrt{2})}{- 3}$

$= \sqrt{3} (\sqrt{10} - \sqrt{3}) - 2 \sqrt{5} (\sqrt{6} - \sqrt{5}) + \sqrt{2} (\sqrt{15} - 3 \sqrt{2})$

$= \sqrt{30} - 3 - 2 \sqrt{30} + 10 + \sqrt{30} - 6$

$= 1$

$=$ R.H.S
Hence proved.

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Similar questions

Q. Show that

\frac{1}{(3 - \sqrt{8})} - \frac{1}{(\sqrt{8} - \sqrt{7})} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - 2} = 5

Q. Simplify :

\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}

Simplify: $\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}$ .

Question 6

Which of the following expressions show that rational numbers are associative under multiplication.
(a) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5}$
(b) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = \frac{2}{3} \times (\frac{3}{5} \times \frac{- 6}{7})$
(c) $\frac{2}{3} \times (\frac{- 6}{7} \times \frac{3}{5}) = (\frac{3}{5} \times \frac{2}{3}) \times \frac{- 6}{7}$
(d) $(\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5} = (\frac{- 6}{7} \times \frac{2}{3}) \times \frac{3}{5}$

Question 6

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Show that 7√3√10+√3−2√5√6+√5−3√2√15+3√2=1

Show that $\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}} = 1$