Question

If the square root of a number is equal to twice the same number what is the number?

Answer 1

`(1)/(4)`

Explanation:

let the number be x , then

`√(x)` = 2x ( square both sides )

x = (2x)² = 4x² ( subtract x from both sides )

4x² - x = 0 ( factor out x from each term )

x(4x - 1) = 0

Equate each factor to zero and solve for x

x = 0

4x - 1 = 0 ⇒ 4x = 1 ⇒ x =
`(1)/(4)`

Assuming x > 0 then the number is
`(1)/(4)`

As a check

`\sqrt{(1)/(4) }` =
`(1)/(2)` and 2 ×
`(1)/(4)` =
`(1)/(2)`