In Exercises 33–44, add or subtract terms whenever possible. 8√5+11√5

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Identify the like terms in the expression. Here, both terms contain the square root of 5, so they are like terms: \(8\sqrt{5}\) and \(11\sqrt{5}\).

Since the terms are like terms, you can add their coefficients (the numbers in front of the square root) together.

Add the coefficients: \(8 + 11\) to get the new coefficient for the combined term.

Write the result as the sum of the coefficients multiplied by the common radical: \((8 + 11)\sqrt{5}\).

Simplify the expression by performing the addition inside the parentheses, resulting in a single term with the square root of 5.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Like Terms in Algebra

Like terms are terms that have the same variable parts raised to the same powers. In expressions involving radicals, like terms have the same radicand (the number inside the square root). Only like terms can be added or subtracted by combining their coefficients.

Simplifying Radicals

Simplifying radicals involves expressing the square root in its simplest form by factoring out perfect squares. This helps identify like terms and makes addition or subtraction possible. For example, √5 is already simplified, so terms with √5 can be combined directly.

Adding and Subtracting Radical Expressions

To add or subtract radical expressions, first ensure the radicals are like terms (same radicand). Then, add or subtract their coefficients just like numerical coefficients. For example, 8√5 + 11√5 equals (8 + 11)√5 = 19√5.