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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