Question

simplify:

1. $sqrt3{-27}$

Explanation:

Step1: Recall cube root property

For a cube root \(\sqrt[3]{a}\), if \(a = b^3\), then \(\sqrt[3]{a}=b\). Also, \(\sqrt[3]{-x}=-\sqrt[3]{x}\) (property of odd roots: \(\sqrt[3]{-a}=-\sqrt[3]{a}\)).

Step2: Factor -27

We know that \(-27 = (-3)\times(-3)\times(-3)=(-3)^3\).

Step3: Apply cube root

Using the cube root property, \(\sqrt[3]{-27}=\sqrt[3]{(-3)^3}\). Since \(\sqrt[3]{b^3}=b\) for any real number \(b\), here \(b = - 3\), so \(\sqrt[3]{(-3)^3}=-3\).

Answer:

\(-3\)