Solve sqrt{75}+sqrt{27}-sqrt{192}

$$\sqrt{ 75 } + \sqrt{ 27 } - \sqrt{ 192 }$$

Evaluate

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Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}+\sqrt{27}-\sqrt{192}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$5\sqrt{3}+3\sqrt{3}-\sqrt{192}$$

Combine 5\sqrt{3} and 3\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}-\sqrt{192}$$

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

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

Combine 8\sqrt{3} and -8\sqrt{3} to get 0.

$$0$$

Factor

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