Question

I need help on this!

Answer 1

Let us solve the given equations.

Consider the equation 1,

`x^2 = 49`

`x = √(49)`

So, x = 7 and -7

Consider the equation 2,

`x^3 = 27`

`x = (27)^ (1)/(3)`

`x = (3^3)^ (1)/(3)`

`x = 3`

Consider the equation 3,

`x^2 = 24`

`x = √(24)`

`x = √(2 * 2 * 2 * 3)`

`x = 2 √(6)`

Consider the equation 4,

`x^3 = -71`

`x = (-71)^ (1)/(3)`

`x = (-1)^(1)/(3) (71)^(1)/(3)`

So,
`x = (-1^3)^(1)/(3) (71)^(1)/(3)`

`x = - (71)^(1)/(3)`

Consider the equation 5,

`x^2 = -25`

`x = √(-25)`

So, x = 5i and -5i

Consider the equation 6,

`x^2 = 85`

`x =√(85)`

`x = √(5 * 17)`

Since, both are prime numbers.

So,
`x =√(85)`