Question

Simplify the expression root 5 (8 + 3 . root 6):

A. 8. root 5 + 3 . root 30
B. 8. root 5 + 3 . root 6
C. 40. root 5 + 3 . root 6
D. 40. root 5 . 18 root 6

Answer 1

To simplify the expression sqrt(5)(8 + 3 sqrt(6)), distribute the square root of 5 to both terms in the parentheses, and then simplify the resulting expression.

Step-by-step explanation:

To simplify the expression sqrt(5)(8 + 3 sqrt(6)), you can distribute the square root of 5 to both terms in the parentheses:

= sqrt(5)(8) + sqrt(5)(3 sqrt(6))

= 8 sqrt(5) + 3 sqrt(5) sqrt(6)

Next, simplify the second term using the property of square roots that allows multiplying under the square root:

= 8 sqrt(5) + 3 sqrt(30)

The simplified expression is 8 sqrt(5) + 3 sqrt(30). Therefore, option A. 8 sqrt(5) + 3 sqrt(30) is the correct choice.