Add or subtract, as indicated. See Example 6. 2√50 - 5√72

Verified step by step guidance

1. First, simplify each square root term separately. Start with $\sqrt{50}$.
2. Recognize that $50=25\times 2$, so $\sqrt{50}=\sqrt{25\times 2}=\sqrt{25}\times \sqrt{2}=5\sqrt{2}$.
3. Next, simplify $\sqrt{72}$. Notice that $72=36\times 2$, so $\sqrt{72}=\sqrt{36\times 2}=\sqrt{36}\times \sqrt{2}=6\sqrt{2}$.
4. Substitute the simplified forms back into the expression: $2\sqrt{50}-5\sqrt{72}=2(5\sqrt{2})-5(6\sqrt{2})$.
5. Combine like terms: $10\sqrt{2}-30\sqrt{2}=(10-30)\sqrt{2}$.

Key Concepts

Simplifying Radicals

Simplifying radicals involves reducing square roots to their simplest form by factoring out perfect squares. For example, √50 can be simplified to √(25*2) = 5√2. This process is essential for performing operations like addition and subtraction with radical expressions.

Combining Like Terms

Combining like terms is a fundamental algebraic principle that allows us to simplify expressions by adding or subtracting coefficients of similar terms. In the context of radicals, this means only terms with the same radical part can be combined, such as 2√2 and 3√2, which would combine to 5√2.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a parenthesis. This property is useful when dealing with expressions that require expansion or simplification, particularly when radicals are involved in addition or subtraction.