Question

Which choice is equivalent to the quotient shown here when x is greater than or equal to 0?

Answer 1

Answer: OPTION C

Explanation:

Remember that:

`\sqrt[n]{a^n}=a`

And the Product of powers property establishes that:

`a^m*a^n=a^((mn))`

Rewrite the expression:

`(√(18x) )/(√(32) )`

Descompose 18 and 32 into their prime factors:

`18=2*3*3=2*3^2\\32=2*2*2*2*2=2^5=2^4*2`

Substitute into the expression, then:

`(√((2*3^2)x) )/(√(2^4*2) )`

Finally,simplifying, you get:

`(3√((2)x) )/(2^2√(2) )=(3√(2x))/(4√(2))=((3)(√(x))(√(2)))/((4)(√(2)))= (3√(x))/(4)`