Question

Find the value of
2 upon under root5-under root3​

Answer 1

Answer:

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Answer 2

Answer:

$\sqrt{5$ + $\sqrt{3}$

Step-by-step explanation:

  2/$\sqrt{5$ - $\sqrt{3}$

By rationalising the denominator

2 ÷ $\sqrt{5$ - $\sqrt{3}$ ×  $\sqrt{5$ + $\sqrt{3}$ ÷ $\sqrt{5$ + $\sqrt{3}$

= 2( $\sqrt{5$ + $\sqrt{3}$ ) ÷ ($\sqrt{5$ - $\sqrt{3}$ ) ($\sqrt{5$ + $\sqrt{3}$)          ∵ { (a – b)(a + b) = a^2 – b^2 }

 = 2( $\sqrt{5$ + $\sqrt{3}$ ) ÷ ( $\sqrt{5$ )^2 - ( $\sqrt{3}$ )^2

 = 2( $\sqrt{5$ + $\sqrt{3}$ ) ÷ 5-3

  = 2( $\sqrt{5$ + $\sqrt{3}$ ) ÷ 2

therefore it is equal to $\sqrt{5$ + $\sqrt{3}$