Question

Add or subtract terms whenever possible. ﻿38−32+372−753\sqrt{8} - \sqrt{32} + 3\sqrt{72} - \sqrt{75}
38​−32​+372​−75​

Accepted Answer

First, rewrite each radical term by factoring the radicand into a product of a perfect square and another factor. For example, express $$\sqrt{8} as$$ $$\sqrt{4 	imes 2}$$, $$\sqrt{32} as$$ $$\sqrt{16 	imes 2}$$, $$\sqrt{72} as$$ $$\sqrt{36 	imes 2}$$, and $$\sqrt{75} as$$ $$\sqrt{25 	imes 3}. $$Next, simplify each radical by taking the square root of the perfect square factor out of the radical. This means $$\sqrt{4 	imes 2} = 2\sqrt{2}$$, $$\sqrt{16 	imes 2} = 4\sqrt{2}$$, $$\sqrt{36 	imes 2} = 6\sqrt{2}$$, and $$\sqrt{25 	imes 3} = 5\sqrt{3}. $$Apply the coefficients outside the radicals to the simplified terms. For example, $$3\sqrt{8}$$ becomes $$3 	imes 2\sqrt{2} = 6\sqrt{2}$$, and $$3\sqrt{72}$$ becomes $$3 	imes 6\sqrt{2} = 18\sqrt{2}. $$Rewrite the entire expression with the simplified terms: $$6\sqrt{2} - 4\sqrt{2} + 18\sqrt{2} - 5\sqrt{3}. $$Finally, combine like terms by adding or subtracting the coefficients of the radicals with the same radicand. Combine the $$\sqrt{2}$$ terms and leave the $$\sqrt{3}$$ term as is, since it has no like terms.

Add or subtract terms whenever possible. $3\(\sqrt{8}\) - \(\sqrt{32}\) + 3\(\sqrt{72}\) - \(\sqrt{75}\)$

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Key Concepts

Simplifying Radicals

Like Radicals

Combining Like Terms

Add or subtract terms whenever possible. 38−32+372−753\(\sqrt{8}\) - \(\sqrt{32}\) + 3\(\sqrt{72}\) - \(\sqrt{75}\)38−32+372−75