Answer:
[tex]12\sqrt{30}[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt{45} \times \sqrt{96}[/tex]
Rewrite 45 as 9 · 5 and 96 as 16 · 6:
[tex]\implies \sqrt{9 \cdot 5} \times \sqrt{16 \cdot 6}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a \cdot b}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{9}\sqrt{5} \times \sqrt{16}\sqrt{6}[/tex]
Rewrite 9 as 3² and 16 as 4²:
[tex]\implies \sqrt{3^2}\sqrt{5} \times \sqrt{4^2}\sqrt{6}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies 3\sqrt{5} \times 4\sqrt{6}[/tex]
Multiply 3 and 4:
[tex]\implies 12\sqrt{5}\sqrt{6}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{a \cdot b}[/tex]
[tex]\implies 12\sqrt{5 \cdot 6}[/tex]
Multiply 5 and 6:
[tex]\implies 12\sqrt{30}[/tex]
