Question

1. simplify.

$xy\sqrt{80}+8x\sqrt{45y^2}-3y\sqrt{125x^2}$
$43xy\sqrt{5}$
$13xy\sqrt{5}$
$28xy^2\sqrt{5}$
$15x^2y\sqrt{5x}$

Explanation:

Step1: Simplify each radical term

Term1: $xy\sqrt{80}$

$\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}$, so $xy\sqrt{80}=4xy\sqrt{5}$

Term2: $8x\sqrt{45y^2}$

$\sqrt{45y^2}=\sqrt{9y^2\times5}=3y\sqrt{5}$, so $8x\sqrt{45y^2}=8x\times3y\sqrt{5}=24xy\sqrt{5}$

Term3: $-3y\sqrt{125x^2}$

$\sqrt{125x^2}=\sqrt{25x^2\times5}=5x\sqrt{5}$, so $-3y\sqrt{125x^2}=-3y\times5x\sqrt{5}=-15xy\sqrt{5}$

Step2: Combine like terms

$4xy\sqrt{5}+24xy\sqrt{5}-15xy\sqrt{5}=(4+24-15)xy\sqrt{5}=13xy\sqrt{5}$

Answer:

$13xy\sqrt{5}$