Question

1. \\(sqrt{5} cdot sqrt{10}\\)
2. \\(sqrt{2} cdot sqrt{10}\\)
3. \\(sqrt{8} cdot sqrt{12}\\)

\\(sqrt{90}\\)

Explanation:

Step1: Multiply radicands (Q7)

$\sqrt{5} \cdot \sqrt{10} = \sqrt{5 \times 10} = \sqrt{50}$

Step2: Simplify radical (Q7)

$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$

Step3: Multiply radicands (Q9)

$\sqrt{2} \cdot \sqrt{10} = \sqrt{2 \times 10} = \sqrt{20}$

Step4: Simplify radical (Q9)

$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$

Step5: Multiply radicands (Q11)

$\sqrt{8} \cdot \sqrt{12} = \sqrt{8 \times 12} = \sqrt{96}$

Step6: Simplify radical (Q11)

$\sqrt{96} = \sqrt{16 \times 6} = 4\sqrt{6}$

Answer:

1. $5\sqrt{2}$
2. $2\sqrt{5}$
3. $4\sqrt{6}$