Question

1. assuming x and y are both positive, write the following expression in simplest radical form. 7xy²√(36x³y²)

Explanation:

Step1: Simplify the square root

Simplify $\sqrt{36x^3y^2}$. We know that $\sqrt{36}=6$, $\sqrt{x^3}=x\sqrt{x}$ (since $x^3 = x^2\cdot x$ and $\sqrt{x^2}=x$ for $x>0$), and $\sqrt{y^2}=y$ (for $y>0$). So $\sqrt{36x^3y^2}=6xy\sqrt{x}$.

Step2: Multiply with the outside term

Now multiply $7xy^2$ with $6xy\sqrt{x}$. Multiply the coefficients: $7\times6 = 42$. Multiply the $x$ terms: $x\times x=x^2$. Multiply the $y$ terms: $y^2\times y = y^3$. Then we have $42x^2y^3\sqrt{x}$.

Answer:

$42x^2y^3\sqrt{x}$