Evaluate 2sqrt27-sqrt3 (A) 5sqrt3 (B)17sqrt3 (C)sqrt24 (D)2sqrt24

Simplify Square Root: Step Title: Simplify the square root of 27 Concise Step Description: Simplify the square root of 27 by finding the largest square factor. Step Calculation: The largest square factor of 27 is 9, which is 3 squared. So, sqrt(27) = sqrt(9 * 3) = sqrt(9) * sqrt(3) = 3sqrt(3). Step Output: 2sqrt(27) simplifies to 2 * 3sqrt(3) = 6sqrt(3).Combine Terms: Step Title: Combine the terms Concise Step Description: Combine the simplified term 6sqrt(3) with -sqrt(3). Step Calculation: 6sqrt(3) - sqrt(3) = (6 - 1)sqrt(3) = 5sqrt(3). Step Output: The expression simplifies to 5sqrt(3).

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Algebra 2

Factor polynomials

Full solution

Q. Evaluate

2\sqrt{27}-\sqrt{3}

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(A)

5\sqrt{3}

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(B)

17\sqrt{3}

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(C)

\sqrt{24}

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(D)

2\sqrt{24}

Simplify Square Root: Step Title: Simplify the square root of $27$ Concise Step Description: Simplify the square root of $27$ by finding the largest square factor. Step Calculation: The largest square factor of $27$ is $9$ , which is $3^2$ . So, $\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$ . Step Output: $2\sqrt{27}$ simplifies to $2 \times 3\sqrt{3} = 6\sqrt{3}$ .
Combine Terms: Step Title: Combine the terms $\newline$ Concise Step Description: Combine the simplified term $6\sqrt{3}$ with $-\sqrt{3}$ . $\newline$ Step Calculation: $6\sqrt{3} - \sqrt{3} = (6 - 1)\sqrt{3} = 5\sqrt{3}$ . $\newline$ Step Output: The expression simplifies to $5\sqrt{3}$ .