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If the AM and HM of two numbers are 27 and 12 respectively, then what is their GM equal to? $\quad[2010-I]$
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Verified Answer
The correct answer is:
18
Given $\mathrm{AM}=27$ and $\mathrm{HM}=12$ and we know that $(\mathrm{GM})^{2}=(\mathrm{AM})(\mathrm{HM})=27 \times 12$
$\Rightarrow G M=\sqrt{27 \times 12}=\sqrt{3 \times 3 \times 3 \times 3 \times 2 \times 2}$
$\Rightarrow \quad \mathrm{GM}=3 \times 3 \times 2=18$
$\Rightarrow G M=\sqrt{27 \times 12}=\sqrt{3 \times 3 \times 3 \times 3 \times 2 \times 2}$
$\Rightarrow \quad \mathrm{GM}=3 \times 3 \times 2=18$
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