Question:
$\sqrt{10} \times \sqrt{15}=?$
(i) $\sqrt{25}$
(ii) $5 \sqrt{6}$
(iii) $6 \sqrt{5}$
(iv) None of these
Solution:
$\sqrt{10} \times \sqrt{15}$
$=\sqrt{2 \times 5} \times \sqrt{3 \times 5}$
$=\sqrt{2} \times \sqrt{5} \times \sqrt{3} \times \sqrt{5} \quad[\sqrt{a b}=\sqrt{a} \times \sqrt{b}]$
$=5 \times \sqrt{2 \times 3}$
$=5 \sqrt{6}$
Hence, the correct answer is option (ii).
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