Simplifying radicals

Question

X^3 + 3 = 0

x^4 + 3 = 0

Answer 1

x³ + 3 = 0

 

 

Subtract 3 on both sides of equation.

 

x³ = -3

 

 

Now, we want to solve for x.  We do something about the exponent on that x.   Raise both sides of the equation by the power of 1/3.

 

 

(x³)^1/3 = (-3)^1/3

 

 

We can multiply exponents.  On the left side, the base is x.  The exponents are 3 and 1/3.  If we multiply the exponents, they cancel each other out, leaving only the base x.

 

 

x = (-3)^1/3

 

 

Now, we use the rule for radicals and exponents.

 

x^1/m  =  ^m√(x)

 

 

Therefore,

 

x = ³√(-3)

 

Since a negative number cubed give is us a negative result,

 

x = - ³√(-3)

 

 

Now use this concept to do the other problem.