Multiple Choice
True or False:
and are equal.
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11. Roots, Radicals, and Complex Numbers
Adding and Subtracting Radicals
Multiple Choice
Add or subtract as indicated and simplify.
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Verified step by step guidance1
Identify the like terms in the expression. Here, both terms contain the square root of 5, so they are like terms and can be combined.
Write the expression by factoring out the common radical: \(2\sqrt{5} + 6\sqrt{5}\) can be seen as \((2 + 6)\sqrt{5}\).
Add the coefficients (the numbers in front of the square root) together: \(2 + 6\).
Multiply the sum of the coefficients by the common radical: \((2 + 6) \times \sqrt{5}\).
Write the simplified expression as the product of the sum and the square root: \(8\sqrt{5}\).