Question

Which of the following is equal to sqrt 18 x^9y^4?

A. 3x^3y^2
B. 3 x^4y^2 sqrt 2x
C. 9 x^3y^2
D. 3 x^3y^2 sqrt 2

Answer 1

Option B is correct

`3\cdot x^4 \cdot y^2 √(2x)`

Explanation:

Given the expression:
`√(18x^9y^4)`

Using exponent rule:

`\sqrt[n]{x^n} = x`

we can write:

18 =
`3 \cdot 3 \cdot 2 = 3^2 \cdot 2`

`x^9 = x^4\cdot x^4 \cdot x`

`y^4 = (y^2)^2`

then;

`√(18x^9y^4)` =
`√(3^2 \cdot 2 \cdot x^4 \cdot x^4 \cdot x \cdot (y^2)^2) = 3\cdot x^4 \cdot y^2 √(2x)`

Therefore, the following is equal to
`√(18x^9y^4)` is
`3\cdot x^4 \cdot y^2 √(2x)`

Answer 2

`\sqrt{18 x^(9) y^(4) } = \\ = \sqrt{9*2 x^(8)*x* y^(4) }= \\ 3 x^(4) y^(2) √(2x)`
Answer: B ) 3x^4y^2sqrt 2x