Explain the difference between solving the equation x = √(16 \:) and \: {x}^(2) = 16

Question

Explain the difference between solving the equation


`x = √(16 \:) and \: {x}^(2) = 16`

Answer 1

`x=√(16)` will give answer x=4

`x^2=16` will give answer x=4 and x= -4

Explanation:

To understand the concept of why this happens, let us try to analyse both the equations.

1.
`x=√(16)`

This equation actually tells that it has already been solved and we just need to tell the answer i.e. x=4. We can see the same by substituting values into x.

if x=4

`4=√(16)` which is a true condition.

if x=-4

`-4=√(16)` which is a false condition.

2.
`x^2=16`

This equation actually tells that it needs solving and we need to find the answer. If we substitute values into x in the equation we have:

if x=4

`x^2=16`

`4^2=16` which is true.

if x=-4

`x^2=16`

`(-4)^2=16` which is also true.

Hence we can see that :

`x^2=16` can give two solutions i.e x=4 and x=-4 and

`x=√(16)` will give answer x=4