Question

Combine and simplify the following radical expression.

Answer 1

`\huge\boxed{24\sqrt5}`

Explanation:

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

`=2\sqrt4\cdot\sqrt5+8\sqrt9\cdot\sqrt5-√(16)\cdot\sqrt5=4\sqrt5+24\sqrt5-4\sqrt5\\\\=(4+24-4)\sqrt5=24\sqrt5`

Answer 2

`24 √(5)`

Explanation:

`2 √(20) + 8 √(45) - √(80)`

`= 2 √(2 * 2 * 5) + 8 √(3 * 3 * 5) - √(2 * 2 * 2 * 2 * 5)`

`= 2(2 √(5) ) + 8(3 √(5) ) - (4 √(5) )`

`= 4 √(5) + 24 √(5) - 4 √(5)`

`= 24 √(5) (ans)`