Respuesta :
Answer:
The simplified form is [tex]8\sqrt[4]{3} [/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]4\sqrt[4]{48}[/tex]
The above expression can be written as:
[tex]4(48)^{\frac{1}{4}}[/tex]
The prime factors of 48 are:
48 = 2×2×2×2×3
Therefore,
[tex]4(2\times 2 \times2 \times 2 \times 3)^{\frac{1}{4}}[/tex]
[tex]4(2^4)^{\frac{1}{4}} \times (3)^{\frac{1}{4}}[/tex]
[tex]4\times2\times (3)^{\frac{1}{4}}[/tex]
[tex]8\times\sqrt[4]{3} [/tex]
[tex]8\sqrt[4]{3} [/tex]
Hence, the simplified form is [tex]8\sqrt[4]{3} [/tex].
