Question

How do you solve `3sqrtk+1=6` and find any extraneous solutions?

Answer 1

`25/9`

Explanation:

We require to isolate the square root term.

subtract 1 from both sides

`rArr3sqrtk+cancel(1)-cancel(1)=6-1rArr3sqrtk=5`

divide both sides by 3

`rArr(cancel(3)^1 sqrtk)/cancel(3)^1=5/3rArrsqrtk=5/3`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtkxxsqrtk=(sqrtk)^2=k)color(white)(a/a)|)))`

Squaring both sides to obtain k

`rArr(sqrtk)^2=(5/3)^2`

`rArrk=5^2/3^2=25/9`

There are no extraneous solutions.