Question
If $$3\sqrt 5 + \sqrt {125} = 17.88{\text{,}}$$ then what will be the value of $$\sqrt {80} $$ $$ + $$ $$6\sqrt 5 $$ = ?
Answer: Option D
$$\eqalign{
& \Rightarrow 3\sqrt 5 + \sqrt {125} = 17.88 \cr
& \Rightarrow {\text{ }}3\sqrt 5 + \sqrt {25 \times 5} = 17.88 \cr
& \Rightarrow {\text{ }}3\sqrt 5 + 5\sqrt 5 = 17.88 \cr
& \Rightarrow {\text{ }}8\sqrt 5 = 17.88 \cr
& \Rightarrow \sqrt 5 = 2.235 \cr
& \therefore \sqrt {80} + 6\sqrt 5 \cr
& = \sqrt {16 \times 5} + 6\sqrt 5 \cr
& = 4\sqrt 5 + 6\sqrt 5 \cr
& = 10\sqrt 5 \cr
& = \left( {10 \times 2.235} \right) \cr
& = 22.35 \cr} $$
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$$\eqalign{
& \Rightarrow 3\sqrt 5 + \sqrt {125} = 17.88 \cr
& \Rightarrow {\text{ }}3\sqrt 5 + \sqrt {25 \times 5} = 17.88 \cr
& \Rightarrow {\text{ }}3\sqrt 5 + 5\sqrt 5 = 17.88 \cr
& \Rightarrow {\text{ }}8\sqrt 5 = 17.88 \cr
& \Rightarrow \sqrt 5 = 2.235 \cr
& \therefore \sqrt {80} + 6\sqrt 5 \cr
& = \sqrt {16 \times 5} + 6\sqrt 5 \cr
& = 4\sqrt 5 + 6\sqrt 5 \cr
& = 10\sqrt 5 \cr
& = \left( {10 \times 2.235} \right) \cr
& = 22.35 \cr} $$
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