Question

show factor tree to receive credit
simplify. \\(sqrt{125}\\)
simplify. \\(sqrt{45}\\)

Explanation:

Simplify $\boldsymbol{\sqrt{125}}$

Step1: Factor 125

Factor 125 into prime factors. $125 = 5\times25$, and $25 = 5\times5$. So, $125 = 5\times5\times5 = 5^2\times5$.

Step2: Simplify the square root

Using the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a\geq0$ and $b\geq0$), we have:
$\sqrt{125}=\sqrt{5^2\times5}=\sqrt{5^2}\times\sqrt{5}$
Since $\sqrt{5^2} = 5$, this simplifies to $5\sqrt{5}$.

Step1: Factor 45

Factor 45 into prime factors. $45 = 9\times5$, and $9 = 3\times3 = 3^2$. So, $45 = 3^2\times5$.

Step2: Simplify the square root

Using the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a\geq0$ and $b\geq0$), we have:
$\sqrt{45}=\sqrt{3^2\times5}=\sqrt{3^2}\times\sqrt{5}$
Since $\sqrt{3^2} = 3$, this simplifies to $3\sqrt{5}$.

Answer:

$5\sqrt{5}$

Simplify $\boldsymbol{\sqrt{45}}$