Question

What is the cube root of $$ 343$$?

Answer 1

$$343=7\times 7\times 7$$

$$\therefore 343={ \left( 7 \right) }^{ 3 }$$

Taking cube roots on both sides,

$$\therefore \sqrt [ 3 ]{ 343 } $$

$$\therefore \sqrt [ 3 ]{ 343 } =\sqrt [ 3 ]{ { \left( 7 \right) }^{ 3 } } $$

$$\therefore \sqrt [ 3 ]{ 343 } ={ \left( { \left( 7 \right) }^{ 3 } \right) }^{ \frac { 1 }{ 3 } }$$

$$\therefore \sqrt [ 3 ]{ 343 } ={ 7 }$$