Question

Combine and simplify the following radical expression.

Answer 1

Answer:

$24 \sqrt{5}$

Step-by-step explanation:

$2 \sqrt{20} + 8 \sqrt{45} - \sqrt{80}$

$= 2 \sqrt{2 \times 2 \times 5} + 8 \sqrt{3 \times 3 \times 5} - \sqrt{2 \times 2 \times 2 \times 2 \times 5}$

$= 2(2 \sqrt{5} ) + 8(3 \sqrt{5} ) - (4 \sqrt{5} )$

$= 4 \sqrt{5} + 24 \sqrt{5} - 4 \sqrt{5}$

$= 24 \sqrt{5} (ans)$

Answer 2

Answer:

$\huge\boxed{24\sqrt5}$

Step-by-step explanation:

$2\sqrt{20}+8\sqrt{45}-\sqrt{80}\\\\=2\sqrt{4\cdot5}+8\sqrt{9\cdot5}-\sqrt{16\cdot5}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5\\\\\text{we know}\ a\sqrt{b}=a\cdot\sqrt{b},\ \text{and}\ \sqrt{a}=b\iff b^2=a\\\\\text{Therefore}\\ 2\sqrt{4}=2\cdot\sqrt4=2\cdot2=4\\8\sqrt9=8\cdot\sqrt9=8\cdot3=24\\\sqrt{16}\cdot\sqrt5=4\cdot\sqrt5=4\sqrt5\\\\\text{Therefore}$

$=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-\sqrt{16}\cdot\sqrt5=4\sqrt5+24\sqrt5-4\sqrt5\\\\=(4+24-4)\sqrt5=24\sqrt5$