Question

HELPP!!!! 100 points. Which expression is equivalent

Answer 1

`\textsf{A.} \quad 2x√(11x)`

Explanation:

Given expression:

`2x√(44x)-2√(11x^3), \;\; \text{if $x > 0$}`

Rewrite 44 as 4 · 11:

`\implies 2x√(4 \cdot 11x)-2√(11x^3)`

Rewrite the exponent 3 as 2+1:

`\implies 2x√(4 \cdot 11x)-2\sqrt{11x^(2+1)}`

`\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c:`

`\implies 2x√(4 \cdot 11x)-2√(11x^2x)}`

`\implies 2x√(4 \cdot 11x)-2√(x^2 \cdot 11x)}`

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

`\implies 2x√(4)√(11x)-2√(x^2)√(11x)`

Rewrite 4 as 2²:

`\implies 2x√(2^2)√(11x)-2√(x^2)√(11x)`

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

`\implies 2x \cdot 2√(11x)-2x√(11x)`

Simplify:

`\implies 4x√(11x)-2x√(11x)`

`\implies 2x√(11x)`