Question

If x2 = 20, what is the value of x?

Answer 1

`x=-2\sqrt5\ and\ x=2\sqrt5`

Explanation:

Given:

The given equation to solve is:

`x^2=20`

In order to solve the above equation, we take square root on both the sides.

While taking square root on both sides, we must consider both positive and negative values. So, this gives:

`√(x^2)=\pm√(20)`

From the definition of square root function, we have

`√(a^2)=a`

Therefore,

`x=\pm√(20)`

Now, writing 20 into the product of its prime factors, we have

`20=2^2* 5`

Therefore,
`x=\pm√(2^2* 5)`

We also know,
`√(a* b)=√(a)*√(b)`

So,
`√(2^2* 5)=√(2^2)* √(5)=2\sqrt5`

Therefore,
`x=\pm2\sqrt5`

So, there are two values of 'x'. They are:

`x=-2\sqrt5\ and\ x=2\sqrt5`