Simplify 56−−√3

Question

Hint: Think about what numbers make up the 56. Do you have 3 of the same that can be taken out and put outside the bracket?

(1 point)
Responses

214−−√3
2 cube root of 14

87–√3
8 cube root of 7

27–√3

Answer 1

To simplify \( \sqrt[3]{56} \), we need to factor 56 into its prime components and see if there are any cubes we can take out of the cube root.

First, we factor 56: \[ 56 = 2^3 \times 7 \]

Now we can rewrite \( \sqrt[3]{56} \): \[ \sqrt[3]{56} = \sqrt[3]{2^3 \times 7} \]

Since \( 2^3 \) is a perfect cube, we can take it out of the cube root: \[ \sqrt[3]{2^3 \times 7} = \sqrt[3]{2^3} \times \sqrt[3]{7} = 2 \times \sqrt[3]{7} \]

Thus, we have: \[ \sqrt[3]{56} = 2 \sqrt[3]{7} \]

Finally, the simplified form of \( \sqrt[3]{56} \) is: \[ 2 \sqrt[3]{7} \]

Therefore, the correct response is: 2 cube root of 14.