Find each root. See Example 3. ∛0.001

검증된 단계별 안내

Recognize that the problem asks for the cube root of 0.001, which means finding a number \( x \) such that \( x^3 = 0.001 \).

Express 0.001 as a power of 10: \( 0.001 = 10^{-3} \). This helps simplify the root calculation using exponent rules.

Use the property of roots and exponents: \( \sqrt[3]{10^{-3}} = 10^{\frac{-3}{3}} \). This means you divide the exponent by the root's degree.

Simplify the exponent: \( 10^{\frac{-3}{3}} = 10^{-1} \).

Rewrite \( 10^{-1} \) as a decimal: \( 10^{-1} = 0.1 \), which is the cube root of 0.001.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Cube Roots

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8. It is denoted as ∛x.

Decimal Representation and Powers of Ten

Understanding decimals and their relation to powers of ten helps simplify root calculations. For instance, 0.001 can be written as 10⁻³, making it easier to apply root operations using exponent rules.

Properties of Exponents in Root Extraction

Roots can be expressed as fractional exponents, such as ∛x = x^(1/3). Applying this property allows converting roots into exponent form, facilitating calculations especially with powers of ten or other numbers.