Question

what value can be placed in front of the radical symbol to make this statement true?
\\(\sqrt3{896} = ? \sqrt3{14}\\)
type your answer in the box below.

Explanation:

Step1: Factorize 896

We need to factorize 896 to express it in terms of a multiple of 14. First, divide 896 by 14: \(896\div14 = 64\). So, \(896=64\times14\).

Step2: Simplify the cube root

Now, rewrite the cube root: \(\sqrt[3]{896}=\sqrt[3]{64\times14}\). Using the property of cube roots \(\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}\) (where \(a = 64\) and \(b = 14\)), we get \(\sqrt[3]{64}\times\sqrt[3]{14}\). Since \(\sqrt[3]{64}=4\) (because \(4^3 = 64\)), this simplifies to \(4\sqrt[3]{14}\).

Answer:

4