Question

what is the following difference?
$11\sqrt{45} - 4\sqrt{5}$
$\circ\\ 7\sqrt{40}$
$\circ\\ 14\sqrt{10}$
$\circ\\ 29\sqrt{5}$
$\circ\\ 95\sqrt{5}$

Explanation:

Step1: Simplify $\sqrt{45}$

We know that $45 = 9\times5$, and $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$). So $\sqrt{45}=\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}$.

Step2: Substitute back into the original expression

The original expression is $11\sqrt{45}-4\sqrt{5}$. Substituting $\sqrt{45}=3\sqrt{5}$, we get $11\times3\sqrt{5}-4\sqrt{5}$.

Step3: Calculate the coefficient

First, calculate $11\times3 = 33$, so the expression becomes $33\sqrt{5}-4\sqrt{5}$. Now, we can combine like terms. For terms with $\sqrt{5}$, we subtract the coefficients: $33 - 4 = 29$. So the result is $29\sqrt{5}$.

Answer:

$29\sqrt{5}$ (corresponding to the option "29√5")