Question

add. write your answer in simple
$8\sqrt{5} + 9\sqrt{20}$

Explanation:

Step1: Simplify $\sqrt{20}$

We know that $20 = 4\times5$, and $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$). So $\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}$.

Step2: Substitute back into the expression

The original expression is $8\sqrt{5}+9\sqrt{20}$. Substituting $\sqrt{20}=2\sqrt{5}$, we get $8\sqrt{5}+9\times2\sqrt{5}$.

Step3: Simplify the second term

Calculate $9\times2\sqrt{5}=18\sqrt{5}$. Now the expression becomes $8\sqrt{5}+18\sqrt{5}$.

Step4: Combine like terms

Since both terms have $\sqrt{5}$, we can add the coefficients: $(8 + 18)\sqrt{5}=26\sqrt{5}$.

Answer:

$26\sqrt{5}$