Question

Which choice is equivalent to the product below? √2 x √5 x √8

A. 16√5
B. 4√20
C. 4√5. <-- correct answer
D. 8√10

Answer 1

`\longrightarrow{\green{ C. \:4 √(5) }}`

`\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}`

`= √(2) * √(5) * √(8)`

`= √(2 * 5 * 8)`

`= √(2 * 5 * 2 * 2 * 2)`

`= √((2 * 2) * (2 * 2) * 5)`

`= \sqrt{ {2}^(2) * {2}^(2) * 5}`

`= \sqrt{ {2}^(2) } * \sqrt{ {2 }^(2) } * √(5)`

`= 2 * 2 √(5)`

`= 4 √(5)`

`\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}`

Answer 2

`\sf Q) √(2) * √(5) * √(8)`

`\sf\implies √(2 * 5 * 8)`

`\sf\implies √(2 * 5 * 2 * 2 * 2)`

`\sf\implies √((2 * 2) * (2 * 2) * 5)`

`\sf\implies \sqrt{ {2}^(2) * {2}^(2) * 5}`

`\sf\implies \sqrt{ {2}^(2) } * \sqrt{ {2 }^(2) } * √(5)`

`\sf\implies 2 * 2 √(5)`

`\sf\implies 4 √(5)`