QuestionAugust 26, 2025

Simplify the radical below. sqrt [4](648) square

Simplify the radical below. sqrt [4](648) square
Simplify the radical below.
sqrt [4](648)
square

Solution
4.1(219 votes)

Answer

3 \times 2^{3/4} Explanation 1. Prime factorization of 648 Factor 648 into primes: 648 = 2^3 \times 3^4. 2. Apply the fourth root to each factor Use \sqrt[4]{a^b} = a^{b/4}: \sqrt[4]{648} = \sqrt[4]{2^3 \times 3^4} = \sqrt[4]{2^3} \times \sqrt[4]{3^4}. 3. Simplify each term \sqrt[4]{2^3} = 2^{3/4} and \sqrt[4]{3^4} = 3^{4/4} = 3. 4. Combine results The expression becomes 3 \times 2^{3/4}.

Explanation

1. Prime factorization of 648<br /> Factor 648 into primes: $648 = 2^3 \times 3^4$.<br />2. Apply the fourth root to each factor<br /> Use $\sqrt[4]{a^b} = a^{b/4}$: $\sqrt[4]{648} = \sqrt[4]{2^3 \times 3^4} = \sqrt[4]{2^3} \times \sqrt[4]{3^4}$.<br />3. Simplify each term<br /> $\sqrt[4]{2^3} = 2^{3/4}$ and $\sqrt[4]{3^4} = 3^{4/4} = 3$.<br />4. Combine results<br /> The expression becomes $3 \times 2^{3/4}$.
Click to rate: