Question
Find the cubic root of 135(1 point)
Responses
5^3√27
5 cube root of 27
3√5
3 square root of 5
^3√5
cube root of 5
3^3√5
Responses
5^3√27
5 cube root of 27
3√5
3 square root of 5
^3√5
cube root of 5
3^3√5
Answers
GPT-4o mini
To find the cubic root of 135, we first break down 135 into its prime factors:
135 = 3 × 45 = 3 × 3 × 15 = 3 × 3 × 3 × 5 = \(3^3 \times 5\).
Now, we can express the cubic root:
\[
\sqrt[3]{135} = \sqrt[3]{3^3 \times 5} = \sqrt[3]{3^3} \times \sqrt[3]{5} = 3\sqrt[3]{5}.
\]
From the given options, the response that corresponds to this is:
**3^3√5** (which may be interpreted as 3 times the cubic root of 5).
Thus, \(3\sqrt[3]{5}\) is the correct answer.
135 = 3 × 45 = 3 × 3 × 15 = 3 × 3 × 3 × 5 = \(3^3 \times 5\).
Now, we can express the cubic root:
\[
\sqrt[3]{135} = \sqrt[3]{3^3 \times 5} = \sqrt[3]{3^3} \times \sqrt[3]{5} = 3\sqrt[3]{5}.
\]
From the given options, the response that corresponds to this is:
**3^3√5** (which may be interpreted as 3 times the cubic root of 5).
Thus, \(3\sqrt[3]{5}\) is the correct answer.