Question

What is the value of x in the equation `sqrt(x- 5) + 7 = 11`?

Answer 1

`x=21`

Explanation:

`color(blue)("Method plan")`
Get the square root on its own on 1 side of the =.

Square both sides so that we can 'get at `x`'

Isolate `x` so that it is one side of the = and everything else on the other side.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering your question")`

Subtract 7 from both sides

`sqrt(x-5)=11-7`

Square both sides

`x-5=4^2`

Add 5 to both sides

`x=21`

Answer 2

x = 21

Explanation:

The first step is to 'isolate' the square root on the left side of the equation.
This is achieved by subtracting 7 from both sides.

`rArrsqrt(x-5)cancel(+7)cancel(-7)=11-7=4`

We now have : `sqrt(x-5)=4 ........ (A)`

`color(orange)"Note"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtaxxsqrta=a" or " (sqrta)^2=a)color(white)(a/a)|)))`

That is when we 'square' a square root we obtain the value inside the square root.
Using this fact in (A) and squaring both sides.

`rArr(sqrt(x-5))^2=4^2`

Thus : x - 5 = 16

Finally, add 5 to both sides to solve for x.

`xcancel(-5)cancel(+5)=16+5rArrx=21`