Question

Which of the following is equivalent to
√20
√5-√4​

Answer 1

SOLUTION

TO DETERMINE

The expression which is equivalent to

$\displaystyle\sf{ \frac{ \sqrt{20} }{ \sqrt{5} - \sqrt{4} } }$

EVALUATION

Here the given expression is

$\displaystyle\sf{ \frac{ \sqrt{20} }{ \sqrt{5} - \sqrt{4} } }$

We simplify it as below

$\displaystyle\sf{ \frac{ \sqrt{20} }{ \sqrt{5} - \sqrt{4} } }$

$\displaystyle\sf{ = \frac{ \sqrt{20} (\sqrt{5} + \sqrt{4} )}{ (\sqrt{5} + \sqrt{4} )(\sqrt{5} - \sqrt{4} ) } }$

$\displaystyle\sf{ = \frac{ \sqrt{100} + \sqrt{80} }{ {( \sqrt{5} )}^{2} - {( \sqrt{4} )}^{2} } }$

$\displaystyle\sf{ = \frac{ \sqrt{10 \times 10} + \sqrt{16 \times 5} }{ 5 - 4 } }$

$\displaystyle\sf{ = \frac{ 10 + 4 \sqrt{5} }{ 1 } }$

$\displaystyle\sf{ = 10 + 4 \sqrt{5} }$

FINAL ANSWER

Hence the equivalent expression is

$\displaystyle\sf{ = 10 + 4 \sqrt{5} }$

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