Question

think now: 12.15.2025
5 of 5
add and/or subtract the given.
\\(\sqrt{96x^7} + \sqrt{54x^7}\\)
\\(12x^3\sqrt{6x}\\)
\\(12x^4\sqrt{6x}\\)
\\(7x^4\sqrt{6x}\\)
\\(7x^3\sqrt{6x}\\)

Explanation:

Step1: Simplify \(\sqrt{96x^7}\)

Factor 96 and \(x^7\): \(96 = 16\times6\), \(x^7 = x^6\times x\). So \(\sqrt{96x^7}=\sqrt{16\times6\times x^6\times x}\). Using \(\sqrt{ab}=\sqrt{a}\sqrt{b}\), we get \(\sqrt{16}\sqrt{x^6}\sqrt{6x}=4x^3\sqrt{6x}\).

Step2: Simplify \(\sqrt{54x^7}\)

Factor 54 and \(x^7\): \(54 = 9\times6\), \(x^7 = x^6\times x\). So \(\sqrt{54x^7}=\sqrt{9\times6\times x^6\times x}\). Using \(\sqrt{ab}=\sqrt{a}\sqrt{b}\), we get \(\sqrt{9}\sqrt{x^6}\sqrt{6x}=3x^3\sqrt{6x}\).

Step3: Add the two simplified radicals

Add \(4x^3\sqrt{6x}\) and \(3x^3\sqrt{6x}\): \((4x^3 + 3x^3)\sqrt{6x}=7x^3\sqrt{6x}\).

Answer:

\(7x^3\sqrt{6x}\) (corresponding to the option \(7x^3\sqrt{6x}\))