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

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Roots of integers

Full solution

Q.

\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 $5 \times \sqrt{5} - 8 \times \sqrt{3}$

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