Question

1. write in simplest form: \\(\sqrt4{720}\\)

Explanation:

Step1: Factorize 720

First, we factorize 720 into prime factors. We know that \(720 = 16\times45\), and further, \(16 = 2^4\) and \(45=9\times5 = 3^2\times5\). So, \(720=2^4\times3^2\times5\).

Step2: Simplify the fourth root

Now, we have \(\sqrt[4]{720}=\sqrt[4]{2^4\times3^2\times5}\). Using the property of radicals \(\sqrt[n]{ab}=\sqrt[n]{a}\times\sqrt[n]{b}\) (for \(a,b\geq0\) and \(n\) a positive integer), we can split this as \(\sqrt[4]{2^4}\times\sqrt[4]{3^2\times5}\). Since \(\sqrt[4]{2^4} = 2\), and \(\sqrt[4]{3^2\times5}=\sqrt[4]{9\times5}=\sqrt[4]{45}\) (because we can't simplify \(\sqrt[4]{45}\) further as 45 has no fourth - power factors). So, \(\sqrt[4]{720}=2\sqrt[4]{45}\).

Answer:

\(2\sqrt[4]{45}\)