Question

Assuming x > 0, which of these expressions is equivalent to 11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third? ?

5 x times the square root of 104 x

20 times the square root of 290 x to the sixth

20 x times the square root of 290 x

104 x times the square root of 5 x

Answer 1

Writing the expression mathematically:
11√(245x³) + 9√(45x³)
11√(7² * 5 * x² * x) + 9√(3² * 5 * x² * x)
77x√(5x) + 27x√(5x)
104x√(5x)

104x times the square root of 5x
The last option is correct.

Answer 2

The answer is 104 x times the square root of 5 x

11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third is:

`11 \sqrt{245 x^(3) } +9 \sqrt{45 x^(3) } =11 √(245) *\sqrt{ x^(3) } +9 √(45) *\sqrt{ x^(3) }= \\ \\ =11 √(5*49) * \sqrt{ x^(2) *x} +9 √(5*9) * \sqrt{ x^(2) *x}= \\ \\ =11* √(5) * √(49) * \sqrt{ x^(2)} * √(x) +9* √(5) * √(9) * \sqrt{ x^(2) }* √(x) = \\ \\ =11* √(5) *7*x* √(x) +9* √(5) *3*x* √(x) = \\ \\ =77x* √(5*x) +27x* √(5*x) = \\ \\ =77x √(5x) +27x √(5x) = \\ \\ =104x √(5x)`