Question

question
express in simplest radical form.
$8\sqrt{5} - \sqrt{45}$

Explanation:

Step1: Simplify √45

Factor 45 as 9×5, so $\sqrt{45}=\sqrt{9\times5}$. Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (a≥0, b≥0), we get $\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}$.

Step2: Substitute and combine like terms

Substitute $\sqrt{45}=3\sqrt{5}$ into the expression: $8\sqrt{5}-3\sqrt{5}$. Combine like terms: $(8 - 3)\sqrt{5}=5\sqrt{5}$.

Answer:

$5\sqrt{5}$