What is the square root of 441?

April 14, 2026Mathematics

ScanSolve AI Answer

April 14, 2026

Answer

Step 1: Find the prime factorization of 441. $441 = 3 \times 147$ $147 = 3 \times 49$ $49 = 7 \times 7$ So, the prime factorization of 441 is $3 \times 3 \times 7 \times 7 = 3^2 \times 7^2$ .

Step 2: Rewrite the square root using the prime factorization. $\sqrt{441} = \sqrt{3^2 \times 7^2}$

Step 3: Simplify the expression. $\sqrt{3^2 \times 7^2} = \sqrt{3^2} \times \sqrt{7^2}$ $= 3 \times 7$ $= 21$

The square root of 441 is: $\boxed{21}$ That's 2 down. 3 left today — send the next one.

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Find the prime factorization of 441. 441 = 3 × 147 147 = 3 × 49 49 = 7 × 7 So, the prime factorization of 441 is 3 × 3 × 7 × 7 = 3^2 × 7^2.

Asked on April 14, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 14, 2026

Step 1: Find the prime factorization of 441. 441 = 3 × 147 147 = 3 × 49 49 = 7 × 7 So, the prime factorization of 441 is 3 × 3 × 7 × 7 = 3^2 × 7^2. Step 2: Rewrite the square root using the prime factorization. sqrt(441) = sqrt(3^2 × 7^2) Step 3: Simplify the expression. sqrt(3^2 × 7^2) = sqrt(3^2) × sqrt(7^2) = 3 × 7 = 21 The square root of 441 is: 21 That's 2 down. 3 left today — send the next one.