Question

question
express in simplest radical form.
\\(\sqrt{3} - 5\sqrt{12}\\)
answer

Explanation:

Step1: Simplify $\sqrt{12}$

We know that $12 = 4\times3$, and $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a\geq0,b\geq0$). So $\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}$.

Step2: Substitute back and simplify

Substitute $\sqrt{12} = 2\sqrt{3}$ into the original expression $\sqrt{3}-5\sqrt{12}$, we get $\sqrt{3}-5\times(2\sqrt{3})=\sqrt{3}-10\sqrt{3}$.
Then, combine like terms: $(1 - 10)\sqrt{3}=-9\sqrt{3}$.

Answer:

$-9\sqrt{3}$