Question
What should come in place of both x in the equation $$\frac{x}{{\sqrt {128} }} = \frac{{\sqrt {162} }}{x}$$
Answer: Option A
$$\eqalign{
& {\text{Let}}\,\frac{x}{{\sqrt {128} }} = \frac{{\sqrt {162} }}{x} \cr
& {\text{Then}}\,{x^2} = \sqrt {128 \times 162} \cr
& = \sqrt {64 \times 2 \times 18 \times 9} \cr
& = \sqrt {{8^2} \times {6^2} \times {3^2}} \cr
& = 8 \times 6 \times 3 \cr
& = 144 \cr
& \therefore x = \sqrt {144} = 12 \cr} $$
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$$\eqalign{
& {\text{Let}}\,\frac{x}{{\sqrt {128} }} = \frac{{\sqrt {162} }}{x} \cr
& {\text{Then}}\,{x^2} = \sqrt {128 \times 162} \cr
& = \sqrt {64 \times 2 \times 18 \times 9} \cr
& = \sqrt {{8^2} \times {6^2} \times {3^2}} \cr
& = 8 \times 6 \times 3 \cr
& = 144 \cr
& \therefore x = \sqrt {144} = 12 \cr} $$
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