How do you simplify 7xsqrt(5xy^2)-sqrt(20x^3y^4)?

Nov 7, 2015

$7 x y \sqrt{5 x} - 2 x {y}^{2} \sqrt{5 x}$

Explanation:

$7 x \sqrt{5 x {y}^{2}} - \sqrt{20 {x}^{3} {y}^{4}}$

Apply the square root rule $\sqrt{{a}^{2}} = a$ to $7 x \sqrt{5 x {y}^{2}}$.

$7 x y \sqrt{5 x} - \sqrt{20 {x}^{3} {y}^{4}}$

Factor $\sqrt{20 {x}^{3} {y}^{4}}$.

$7 x y \sqrt{5 x} - \sqrt{2 \cdot 2 \cdot 5 \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y}$

Pair like terms.

$7 x y \sqrt{5 x} - \sqrt{5 x \left(2 \cdot 2\right) \left(x \cdot x\right) \left(y \cdot y\right) \left(y \cdot y\right)}$

Simplify.

$7 x y \sqrt{5 x} - \sqrt{5 x \cdot {2}^{2} \cdot {x}^{2} \cdot {y}^{2} \cdot {y}^{2}}$

Apply the square root rule $\sqrt{{a}^{2}} = a$.

$7 x y \sqrt{5 x} - 2 \cdot x \cdot y \cdot y \sqrt{5 x}$

Simplify.

$7 x y \sqrt{5 x} - 2 x {y}^{2} \sqrt{5 x}$