Question
If $$\sqrt 5 = 2.236{\text{,}}$$ then the value of $$\frac{{\sqrt 5 }}{2} \, - $$ $$\frac{{10}}{{\sqrt 5 }} \, + $$ $$\sqrt {125} $$ is equal to = ?
Answer: Option B
$$\eqalign{
& = \frac{{\sqrt 5 }}{2} - \frac{{10}}{{\sqrt 5 }} + \sqrt {125} \cr
& = \frac{{{{\left( {\sqrt 5 } \right)}^2} - 20 + 2\sqrt 5 \times 5\sqrt 5 }}{{2\sqrt 5 }} \cr
& = \frac{{5 - 20 + 50}}{{2\sqrt 5 }} \cr
& = \frac{{35}}{{2\sqrt 5 }} \times \frac{{\sqrt 5 }}{{\sqrt 5 }} \cr
& = \frac{{35\sqrt 5 }}{{10}} \cr
& = \frac{7}{2} \times 2.236 \cr
& = 7 \times 1.118 \cr
& = 7.826 \cr} $$
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$$\eqalign{
& = \frac{{\sqrt 5 }}{2} - \frac{{10}}{{\sqrt 5 }} + \sqrt {125} \cr
& = \frac{{{{\left( {\sqrt 5 } \right)}^2} - 20 + 2\sqrt 5 \times 5\sqrt 5 }}{{2\sqrt 5 }} \cr
& = \frac{{5 - 20 + 50}}{{2\sqrt 5 }} \cr
& = \frac{{35}}{{2\sqrt 5 }} \times \frac{{\sqrt 5 }}{{\sqrt 5 }} \cr
& = \frac{{35\sqrt 5 }}{{10}} \cr
& = \frac{7}{2} \times 2.236 \cr
& = 7 \times 1.118 \cr
& = 7.826 \cr} $$
Was this answer helpful ?
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