Identify Roots Quick Check

2 of 52 of 5 Items
Question
Find the cubic root of 96.(1 point)
Responses

2^3√7
2 root index 3 start root 7 end root

2^3√12
2 root index 3 start root 12 end root

2√12
2 start root 12 end root

4√6
4 start root 6 end root
Skip to navigation

1 answer

To find the cubic root of 96, we can express 96 in terms of its prime factors and then simplify.

The prime factorization of 96 is: \( 96 = 2^5 \times 3^1 \)

To find the cubic root (the cube root), we can write: \[ \sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} \] This can be simplified using the property of exponents: \[ \sqrt[3]{96} = \sqrt[3]{2^3 \times 2^2 \times 3^1} = \sqrt[3]{2^3} \cdot \sqrt[3]{2^2} \cdot \sqrt[3]{3} \] Since \( \sqrt[3]{2^3} = 2 \), we have: \[ \sqrt[3]{96} = 2 \cdot \sqrt[3]{4 \times 3} = 2 \cdot \sqrt[3]{12} \]

Therefore, the cubic root of 96 is: \[ 2 \sqrt[3]{12} \]

From the options given, the correct response is: 2 root index 3 start root 12 end root

So, the correct answer is: 2√12 (expressed as cubic root).

Similar Questions
  1. Identify Roots Quick Check3 of 53 of 5 Items Question Find the cubic root of 189.(1 point) Responses 27^3√7 27 root index 3
    1. answers icon 1 answer
    1. answers icon 9 answers
    1. answers icon 5 answers
  2. Identify Roots Quick Check4 of 54 of 5 Items Question Find the square root of 250.(1 point) Responses 5√10 5 start root 10 end
    1. answers icon 1 answer
more similar questions