Question

5. Solve this question step by step
Please give verified answer​

Answer 1

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• A fraction

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$\red{\underline \bold{To \: Find:}}$

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• Rationalize the denominator.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\sf \longmapsto \dfrac { 5 } { 4 \sqrt2 + 3 \sqrt3}$

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We need to apply some properties so that the denominator gets a rational number.

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$\sf \longmapsto \dfrac { 5 } { 4 \sqrt2 + 3 \sqrt3} \times \dfrac { 4 \sqrt2 - 3 \sqrt3 } { 4 \sqrt2 - 3 \sqrt3}$

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$\sf \longmapsto \dfrac { 5(4 \sqrt2 - 3 \sqrt3) } { (4 \sqrt2)^2 - (3 \sqrt3)^2}$

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$\sf \longmapsto \dfrac { 20 \sqrt 2 - 15 \sqrt 3 } { 32 - 27 }$

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$\sf \longmapsto \dfrac { 20 \sqrt 2 - 15 \sqrt 3 } { 5 }$

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$\sf \longmapsto \dfrac { \cancel {5}(4 \sqrt 2 - 3 \sqrt 3 } { \cancel {5} }$

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$\red{\sf \longmapsto 4 \sqrt 2 - 3 \sqrt 3}$

$\rule{200}5$