Question

Offering 100 points for help with this one.

Answer 1

5
`√(5x)`

Explanation:

`√(320x)` = 8
`√(5)`
`√(x)`

`√(45x)` = 3
`√(5)`
`√(x)`

and then just subtract them

Answer 2

`5√(5x)`

Explanation:

Given expression:

`√(320x)-√(45x)`

Rewrite 320 as 64 · 5 and rewrite 45 as 9 · 5:

`\implies √(64 \cdot 5 \cdot x)-√(9 \cdot 5 \cdot x)`

`\textsf{Apply the radical rule} \quad √(ab)=√(a)√(b):`

`\implies √(64) √(5x)-√(9) √(5x)`

Rewrite 64 as 8² and 9 as 3²:

`\implies √(8^2) √(5x)-√(3^2) √(5x)`

`\textsf{Apply the radical rule} \quad √(a^2)=a, \quad a \geq 0:`

`\implies 8√(5x)-3√(5x)`

Factor out the common term
`√(5x)`:

`\implies (8-3)√(5x)`

Subtract the numbers:

`\implies 5√(5x)`