Question

Which expression is equivalent to sqrt8x^7y^8? assume x>0

Answer 1

Answer: It is C or 2x^3y^4 square root2x.

Step-by-step explanation: Checked on my calculator it is correct.

Answer 2

`\sqrt{8x^7y^8`
`= 2x^3y^4 * √(2x)`

Explanation:

Given

`\sqrt{8x^7y^8`

Required

Evaluate

`\sqrt{8x^7y^8`

Separate each factor with multiplication sign

`\sqrt{8*x^7*y^8`

Express 8 as 4 * 2 and
`x^7` as
`x^6 * x`

`\sqrt{4 * 2 *x^6 * x*y^8`

Split each factor

`√(4) * √(2) *√(x^6) * √(x)*√(y^8)`

Evaluate
`\sqrt4`

`2 * √(2) *√(x^6) * √(x)*√(y^8)`

Apply law of indices:

`2 * √(2) * x^{6*(1)/(2)} * √(x) * y^{8*(1)/(2)}`

`2 * √(2) * x^3 * √(x) * y^4`

Reorder

`2* x^3 * y^4 * √(2) * √(x)`

`2x^3y^4 * √(2) * √(x)`

`2x^3y^4 * √(2*x)`

`2x^3y^4 * √(2x)`

`2x^3y^4 \sqrt {2x`

Hence:

`\sqrt{8x^7y^8`
`= 2x^3y^4 * √(2x)`