Question

u5d1: rational exponents
score: 13/28 answered: 16/28
question 11
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\sqrt3{-1000}
27 ×
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Explanation:

Step1: Recall cube root definition

The cube root of a number \( x \), denoted as \( \sqrt[3]{x} \), is a number \( y \) such that \( y^3 = x \). Also, for negative numbers, \( \sqrt[3]{-a}=-\sqrt[3]{a} \) (since \((-y)^3=-y^3\)).

Step2: Find the cube root of 1000

We know that \( 10^3 = 10\times10\times10 = 1000 \), so \( \sqrt[3]{1000}=10 \).

Step3: Apply the negative sign rule

Using the rule \( \sqrt[3]{-a}=-\sqrt[3]{a} \), we have \( \sqrt[3]{-1000}=-\sqrt[3]{1000} \).
Substituting \( \sqrt[3]{1000} = 10 \), we get \( -\sqrt[3]{1000}=-10 \).

Answer:

\(-10\)