Question

Simplify the expression

Answer 1

Answer:
$3 \sqrt{2} x^2 y^{3/2}$
This can be rewritten as:
$3x^2 \sqrt{2y^3}$

Explanation:
Before we begin, remember the following:
√ab = √a * √b
√xᵃ = x^(a/2)

Now, for the given, we have:
$\sqrt{18x^4y^3}$

18 can be rewritten as 9 * 2
Therefore, the given expression would now become:
$\sqrt{9*2x^4y^3}$

Distributing the root as mentioned in the above rules, we would get:
$\sqrt{9} * \sqrt{2} * \sqrt{x^4} * \sqrt{y^3}$

We know that:
$\sqrt{9} = 3$ (we would disregard the negative value of the root)
$\sqrt{x^4} = x^{4/2} = x^2$
$\sqrt{y^3} = y^{3/2}$

Substitute with the above in the expression, we would get the final answer:
$3 \sqrt{2} x^2 y^{3/2}$
This can be rewritten as:
$3x^2 \sqrt{2y^3}$

Hope this helps :)

Answer 2

√18x^4y^3
= 3x^2y√(2y)

hope it helps