Question

Multiply and Simplify
√45 x √96

Answer 1

`{ \qquad\qquad\huge\underline{{\sf Answer}}}`

Let's get it done ~

`\qquad \sf  \dashrightarrow \: √(45) * √(96)`

`\qquad \sf  \dashrightarrow \: \sqrt{ {3}^(2) * 5 } * \sqrt{2 {}^(4) * 2 * 3}`

`\qquad \sf  \dashrightarrow \: 3 √(5) * 2 {}^(2) √(6)`

`\qquad \sf  \dashrightarrow \: 3 √(5) * 4√(6)`

`\qquad \sf  \dashrightarrow \: 12 √(30)`

Answer 2

`12√(30)`

Explanation:

Given:

`√(45) * √(96)`

Rewrite 45 as 9 · 5 and 96 as 16 · 6:

`\implies √(9 \cdot 5) * √(16 \cdot 6)`

`\textsf{Apply radical rule} \quad √(a \cdot b)=√(a)√(b):`

`\implies √(9)√(5) * √(16)√(6)`

Rewrite 9 as 3² and 16 as 4²:

`\implies √(3^2)√(5) * √(4^2)√(6)`

`\textsf{Apply radical rule} \quad √(a^2)=a, \quad a \geq 0`

`\implies 3√(5) * 4√(6)`

Multiply 3 and 4:

`\implies 12√(5)√(6)`

`\textsf{Apply radical rule} \quad √(a)√(b)=√(a \cdot b)`

`\implies 12√(5 \cdot 6)`

Multiply 5 and 6:

`\implies 12√(30)`