Questions: Write the following in simplified radical form. sqrt[4]96

Transcript text: Write the following in simplified radical form. \[ \sqrt[4]{96} \]

Solution

Solution Steps

Step 1: Factorize the number under the radical

First, factorize $96$ into its prime factors: $96 = 2^5 \times 3$

Step 2: Rewrite the radical using the prime factors

Express $\sqrt[4]{96}$ using the prime factorization: $\sqrt[4]{96} = \sqrt[4]{2^5 \times 3}$

Step 3: Simplify the radical

Break down the expression by separating the exponents that are multiples of 4: $\sqrt[4]{2^5 \times 3} = \sqrt[4]{2^4 \times 2 \times 3} = \sqrt[4]{2^4} \times \sqrt[4]{2 \times 3}$ $= 2 \times \sqrt[4]{6}$

Final Answer

$\boxed{2\sqrt[4]{6}}$

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