Question

match the given radical expression to its simplest form. √128 2√125x³ 5√27x²y⁵ possible points: 1 5x√5x 8√2 15xy²√3y 64√2 3xy√3y 15xy√3y 10x√5x

Explanation:

Step1: Simplify $\sqrt{128}$

Factor 128: $128 = 64\times2$. Then $\sqrt{128}=\sqrt{64\times2}=\sqrt{64}\times\sqrt{2}=8\sqrt{2}$.

Step2: Simplify $2\sqrt{125x^3}$

Factor 125 and $x^3$: $125 = 25\times5$, $x^3 = x^2\times x$. So $\sqrt{125x^3}=\sqrt{25\times5\times x^2\times x}=\sqrt{25}\times\sqrt{x^2}\times\sqrt{5x}=5x\sqrt{5x}$. Then $2\sqrt{125x^3}=2\times5x\sqrt{5x}=10x\sqrt{5x}$.

Step3: Simplify $5\sqrt{27x^2y^5}$

Factor 27, $x^2$, and $y^5$: $27 = 9\times3$, $y^5 = y^4\times y$. So $\sqrt{27x^2y^5}=\sqrt{9\times3\times x^2\times y^4\times y}=\sqrt{9}\times\sqrt{x^2}\times\sqrt{y^4}\times\sqrt{3y}=3xy^2\sqrt{3y}$. Then $5\sqrt{27x^2y^5}=5\times3xy^2\sqrt{3y}=15xy^2\sqrt{3y}$.

Answer:

$\sqrt{128}$ matches $8\sqrt{2}$
$2\sqrt{125x^3}$ matches $10x\sqrt{5x}$
$5\sqrt{27x^2y^5}$ matches $15xy^2\sqrt{3y}$