(n) Which expression shows the surds written in their simplest form? sqrt125-sqrt192=

Evaluate sqrt(125): Evaluate: sqrt(125) 125 can be factored into 5 * 5 * 5. Since 5 * 5 = 25, we can take the square root of 25 out of the square root of 125. sqrt(125) = sqrt(25 * 5) = sqrt(25) * sqrt(5) = 5 * sqrt(5)Evaluate sqrt(192: Evaluate: sqrt(192) 192 can be factored into 64 * 3. Since 64 is a perfect square (8 * 8), we can take the square root of 64 out of the square root of 192. sqrt(192) = sqrt(64 * 3) = sqrt(64) * sqrt(3) = 8 * sqrt(3)Combine simplified surds: Combine the two simplified surds. The expression becomes 5 * sqrt(5) - 8 * sqrt(3)

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$\sqrt{125} - \sqrt{192}$ =

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\sqrt{125} - \sqrt{192}

Evaluate $\sqrt{125}$ : Evaluate: $\sqrt{125}$ $125$ can be factored into $5 \times 5 \times 5$ .Since $5 \times 5 = 25$ , we can take the square root of $25$ out of the square root of $125$ . $\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5 \times \sqrt{5}$
Evaluate $\sqrt{192}$ : Evaluate: $\sqrt{192}$ $192$ can be factored into $64 \times 3$ . Since $64$ is a perfect square ( $8 \times 8$ ), we can take the square root of $64$ out of the square root of $192$ . $\sqrt{192} = \sqrt{64 \times 3} = \sqrt{64} \times \sqrt{3} = 8 \times \sqrt{3}$
Combine simplified surds: Combine the two simplified surds. The expression becomes $5 \times \sqrt{5} - 8 \times \sqrt{3}$