Simplify 2-3-52-2-3-3-

2√(3) √(5)2√(2)+3√(3)×2√(2) 3√(3)2√(2) 3√(3) =4√(6) 6√(9) 2√(10)+3√(15)(2√(2))^2 (3√(3))^2 =4√(6) 18 2√(10)+3√(15)8 27 =4√(6) 18 2√(10)+3√(15) 19 = (4√(6) ...

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Byju's Answer

Standard IX

Mathematics

Rationalisation

Simplify 2√3-...

Question

$Simplify \frac{2 \sqrt{3} - \sqrt{5}}{2 \sqrt{2} + 3 \sqrt{3}} .$

\frac{18 + 2 \sqrt{10} - 4 \sqrt{6} - 3 \sqrt{15}}{19}

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\frac{18 + 4 \sqrt{6}}{19}

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\frac{2 \sqrt{10} - 3 \sqrt{15}}{23}

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\frac{18 + 2 \sqrt{10} + 3 \sqrt{15}}{19}

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Solution

The correct option is A
$\frac{18 + 2 \sqrt{10} - 4 \sqrt{6} - 3 \sqrt{15}}{19}$
$\frac{2 \sqrt{3} - \sqrt{5}}{2 \sqrt{2} + 3 \sqrt{3}} \times \frac{2 \sqrt{2} - 3 \sqrt{3}}{2 \sqrt{2} - 3 \sqrt{3}} = \frac{4 \sqrt{6} - 6 \sqrt{9} - 2 \sqrt{10} + 3 \sqrt{15}}{(2 \sqrt{2})^{2} - (3 \sqrt{3})^{2}} = \frac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15}}{8 - 27} = \frac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15}}{- 19} = \frac{- (4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15})}{19} = \frac{- 4 \sqrt{6} + 18 + 2 \sqrt{10} - 3 \sqrt{15}}{19} = \frac{18 + 2 \sqrt{10} - 4 \sqrt{6} - 3 \sqrt{15}}{19}$

So, option a is correct.

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Similar questions

Q. Simplify
2+2=

Simplify:

(i) $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} + \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$

(ii) $\frac{1}{2 + \sqrt{3}} + \frac{2}{\sqrt{5} - \sqrt{3}} + \frac{1}{2 - \sqrt{5}}$

(iii) $\frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} - \frac{3}{\sqrt{5} + \sqrt{2}}$

Simplify :

(i) $\frac{3 \sqrt{2} - 2 \sqrt{3}}{3 \sqrt{2} + 2 \sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}$

(ii) $\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}}$

Q. Evaluate

\frac{\sqrt{5}}{\sqrt{3} + \sqrt{2}} - \frac{3 \sqrt{3}}{\sqrt{5} + \sqrt{2}} + \frac{2 \sqrt{2}}{\sqrt{5} + \sqrt{3}}

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) $(\frac{2}{3} \times \frac{- 6}{7}) \times \frac{3}{5} = (\frac{- 6}{7} \times \frac{2}{3}) \times \frac{3}{5}$

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Simplify 2√3−√52√2+3√3.

$Simplify \frac{2 \sqrt{3} - \sqrt{5}}{2 \sqrt{2} + 3 \sqrt{3}} .$