Question

add. write your answer in simplest form.
$8\sqrt{12} + 7\sqrt{3}$

Explanation:

Step1: Simplify $\sqrt{12}$

We know that $12 = 4\times3$, so $\sqrt{12}=\sqrt{4\times3}$. By the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 4$, $b = 3$ and $a\geq0,b\geq0$), we have $\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}$. Since $\sqrt{4} = 2$, then $\sqrt{12}=2\sqrt{3}$.

Step2: Substitute back into the original expression

The original expression is $8\sqrt{12}+7\sqrt{3}$. Substituting $\sqrt{12}=2\sqrt{3}$ into it, we get $8\times(2\sqrt{3})+7\sqrt{3}$.

Step3: Simplify the first term

Calculate $8\times(2\sqrt{3})$. $8\times2 = 16$, so $8\times(2\sqrt{3})=16\sqrt{3}$. Now the expression becomes $16\sqrt{3}+7\sqrt{3}$.

Step4: Combine like terms

Since both terms have $\sqrt{3}$, we can combine them. Using the rule $a\sqrt{c}+b\sqrt{c}=(a + b)\sqrt{c}$ (where $a = 16$, $b = 7$, $c = 3$), we have $(16 + 7)\sqrt{3}=23\sqrt{3}$.

Answer:

$23\sqrt{3}$