To evaluate [tex]\( 49^{\frac{1}{3}} \)[/tex], we are looking for the cube root of 49. This means we need to find a number which, when multiplied by itself three times, equals 49.
To understand this better, let's denote our desired number as [tex]\( x \)[/tex]. Thus, we need to solve the equation:
[tex]\[ x^3 = 49 \][/tex]
Taking the cube root of both sides of the equation, we get:
[tex]\[ x = 49^{\frac{1}{3}} \][/tex]
This process essentially involves finding the cubic root of 49. After performing the appropriate computation, we obtain the following result:
[tex]\[ 49^{\frac{1}{3}} \approx 3.6593057100229713 \][/tex]
So, the value of [tex]\( 49^{\frac{1}{3}} \)[/tex] is approximately [tex]\( 3.6593057100229713 \)[/tex].
