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

$\longrightarrow{\green{ C. \:4 \sqrt{5} }}$ 

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

$= \sqrt{2} \times \sqrt{5} \times \sqrt{8}$

$= \sqrt{2 \times 5 \times 8}$

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

$= \sqrt{(2 \times 2) \times (2 \times 2) \times 5}$

$= \sqrt{ {2}^{2} \times {2}^{2} \times 5}$

$= \sqrt{ {2}^{2} } \times \sqrt{ {2 }^{2} } \times \sqrt{5}$

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

$= 4 \sqrt{5}$

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

Answer 2

$\sf Q) \sqrt{2} \times \sqrt{5} \times \sqrt{8}$

$\sf\implies \sqrt{2 \times 5 \times 8}$

$\sf\implies \sqrt{2 \times 5 \times 2 \times 2 \times 2}$

$\sf\implies \sqrt{(2 \times 2) \times (2 \times 2) \times 5}$

$\sf\implies \sqrt{ {2}^{2} \times {2}^{2} \times 5}$

$\sf\implies \sqrt{ {2}^{2} } \times \sqrt{ {2 }^{2} } \times \sqrt{5}$

$\sf\implies 2 \times 2 \sqrt{5}$

$\sf\implies 4 \sqrt{5}$