Question

7 what is the simplified form of $sqrt{48x^{2}y^{3}}$?
a $4xysqrt{3y}$
b $4xysqrt{3}$
c $2xysqrt{12y}$
d $4xysqrt{12y}$

Explanation:

Step1: Factorize 48

We know that $48 = 16\times3$, so $\sqrt{48x^{2}y^{3}}=\sqrt{16\times3\times x^{2}\times y^{2}\times y}$.

Step2: Apply square - root property

According to the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a\geq0,b\geq0$), we have $\sqrt{16\times3\times x^{2}\times y^{2}\times y}=\sqrt{16}\times\sqrt{3}\times\sqrt{x^{2}}\times\sqrt{y^{2}}\times\sqrt{y}$.

Step3: Simplify each square - root

Since $\sqrt{16} = 4$, $\sqrt{x^{2}}=|x|$ (assuming real - valued variables, and if we assume $x\geq0$ for simplicity in the context of simplification), $\sqrt{y^{2}} = y$, then $\sqrt{16}\times\sqrt{3}\times\sqrt{x^{2}}\times\sqrt{y^{2}}\times\sqrt{y}=4xy\sqrt{3y}$.

Answer:

A. $4xy\sqrt{3y}$