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

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

Answer 2

Answer:

Option B is correct

$3\cdot x^4 \cdot y^2 \sqrt{2x}$

Step-by-step explanation:

Given the expression: $\sqrt{18x^9y^4}$

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;

$\sqrt{18x^9y^4}$ = $\sqrt{3^2 \cdot 2 \cdot x^4 \cdot x^4 \cdot x \cdot (y^2)^2} = 3\cdot x^4 \cdot y^2 \sqrt{2x}$

Therefore, the following is equal to $\sqrt{18x^9y^4}$ is $3\cdot x^4 \cdot y^2 \sqrt{2x}$