Video: Evaluating Cube Roots

Evaluate ∛(64/343).

01:46

Video Transcript

Evaluate the cube root of 64 over 343.

In order to solve this problem, I’m actually gonna use this relationship, which is that the cube root of 𝑎 over 𝑏 is the same as the cube root of 𝑎 divided by the cube root of 𝑏. So we have the cube root of 64 divided by the cube root of 343.

As a numerator, we have to cube root 64 or to say the cube root of 64 is actually equal to four. And that’s because four multiplied by four multiplied by four is equal to 64. And that’s cause we get four multiplied by four is 16. 16 multiplied by four is equal to 64.

Okay, so that’s the numerator. Well, on our denominator, we actually have the cube root of 343. We know this is gonna be equal to seven. And then, again, we know this because seven multiplied by seven multiplied by seven is equal to 343. And that’s because seven multiplied by seven is 49 and then multiplied by another seven is equal to 343.

Okay, great, it’s actually worth noting at this point that we don’t have to worry about negative answers. And that’s because if we have a negative multiplied by a negative multiplied by a negative and the result is negative and as both our 64 and our 343 are both positive, then therefore, the cube root of either of these cannot be a negative number. So therefore, we can say that if we evaluate the cube root of 64 over 343, our answer is four over seven.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.