Which of the following equivalent form of 3 -6-4 -3-4 -6-2 -3 -

The correct option is A 8 5√(2)/14Rationalising the denominator of 3√(6) 4√(3)/4√(6) 2√(3), we get: 3√(6) 4√(3)/4√(6) 2√(3) = 3√(6) 4√(3)/4√(6) 2√(3)×4√(6)+2√( ...

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Byju's Answer

Standard IX

Mathematics

Rationalising Factor

Which of the ...

Question

Which of the following equivalent form of $\frac{3 \sqrt{6} - 4 \sqrt{3}}{4 \sqrt{6} - 2 \sqrt{3}} ?$

\frac{8 - 5 \sqrt{2}}{14}

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\frac{5 - 8 \sqrt{2}}{14}

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\frac{8 - 5 \sqrt{2}}{18}

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\frac{5 - 8 \sqrt{2}}{18}

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Solution

The correct option is A $\frac{8 - 5 \sqrt{2}}{14}$
Rationalising the denominator of $\frac{3 \sqrt{6} - 4 \sqrt{3}}{4 \sqrt{6} - 2 \sqrt{3}},$ we get:
$\frac{3 \sqrt{6} - 4 \sqrt{3}}{4 \sqrt{6} - 2 \sqrt{3}} = \frac{3 \sqrt{6} - 4 \sqrt{3}}{4 \sqrt{6} - 2 \sqrt{3}} \times \frac{4 \sqrt{6} + 2 \sqrt{3}}{4 \sqrt{6} + 2 \sqrt{3}}$
$= \frac{(12 \times 6) - 16 \sqrt{18} - (8 \times 3)}{96 - 12}$
$= \frac{48 - 30 \sqrt{2}}{84}$
$= \frac{8 - 5 \sqrt{2}}{14}$

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Similar questions

Q. Find the equivalent form of

\frac{4 \sqrt{2} + 3 \sqrt{6}}{5 \sqrt{6} + 6 \sqrt{2}}

Q. Are

\frac{- 2}{3}

and

\frac{- 4}{6}

equivalent?

Q. A ratio equivalent of 2 : 3 is

(a) 4 : 3
(b) 2 : 6
(c) 6 : 9
(d) 10 : 9

\frac{2}{3}

and

\frac{4}{6}

are equivalent rational numbers.

Q. Simplify the following:

\frac{6}{2 \sqrt{3} - \sqrt{6}} + \frac{\sqrt{6}}{\sqrt{3} + \sqrt{2}} - \frac{4 \sqrt{3}}{\sqrt{6} - \sqrt{2}}

= ?

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Which of the following equivalent form of 3√6−4√34√6−2√3?

The correct option is A 8−5√214Rationalising the denominator of 3√6−4√34√6−2√3, we get: 3√6−4√34√6−2√3=3√6−4√34√6−2√3×4√6+2√34√6+2√3 =(12×6)−16√18−(8×3)96−12 =48−30√284 =8−5√214

Which of the following equivalent form of $\frac{3 \sqrt{6} - 4 \sqrt{3}}{4 \sqrt{6} - 2 \sqrt{3}} ?$