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9sqrt12+5sqrt32-sqrt72

$31$ . $9 \sqrt{12}+5 \sqrt{32}-\sqrt{72}$

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Factor polynomials

Full solution

Q.

31

.

9 \sqrt{12}+5 \sqrt{32}-\sqrt{72}

Simplify Square Roots: Step Title: Simplify the Square Roots $\newline$ Concise Step Description: Simplify each square root term by finding the largest perfect square factor. $\newline$ Step Calculation: $\newline$ - The largest perfect square factor of $12$ is $4$ , so $\sqrt{12} = \sqrt{(4\times3)} = 2\sqrt{3}$ . $\newline$ - The largest perfect square factor of $32$ is $16$ , so $\sqrt{32} = \sqrt{(16\times2)} = 4\sqrt{2}$ . $\newline$ - The largest perfect square factor of $72$ is $36$ , so $\sqrt{72} = \sqrt{(36\times2)} = 6\sqrt{2}$ . $\newline$ Step Output: $9\sqrt{12} = 9\times2\sqrt{3} = 18\sqrt{3}$ , $4$ $0$ , $4$ $1$
Combine Like Terms: Step Title: Combine Like Terms $\newline$ Concise Step Description: Combine the terms with the same radical part. $\newline$ Step Calculation: $\newline$ - There are no like terms to combine since each term has a different radical part. $\newline$ Step Output: The expression remains as $18\sqrt{3} + 20\sqrt{2} - 6\sqrt{2}$ .
Subtract Same Radical: Step Title: Subtract the Square Root Terms with the Same Radical $\newline$ Concise Step Description: Subtract the terms with the same radical part. $\newline$ Step Calculation: $\newline$ - Subtract the coefficients of the terms with $\sqrt{2}$ : $20\sqrt{2} - 6\sqrt{2} = 14\sqrt{2}$ . $\newline$ Step Output: The simplified expression is $18\sqrt{3} + 14\sqrt{2}$ .

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