Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2

검증된 단계별 안내

Identify the expression to simplify: \(\frac{5}{\sqrt{2}}\).

Recognize that the denominator contains a square root, which is often rationalized to eliminate the radical from the denominator.

Multiply both the numerator and the denominator by \(\sqrt{2}\) to rationalize the denominator: \(\frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\).

Apply the multiplication: the numerator becomes \(5 \times \sqrt{2}\) and the denominator becomes \(\sqrt{2} \times \sqrt{2} = 2\), so the expression is now \(\frac{5 \sqrt{2}}{2}\).

The expression \(\frac{5 \sqrt{2}}{2}\) is the simplified form with a rationalized denominator.

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주요 개념

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

Simplifying Radicals

Simplifying radicals involves rewriting a square root or other root expression in its simplest form. This often means factoring out perfect squares from under the radical or rationalizing denominators to eliminate roots from the denominator.

Rationalizing the Denominator

Rationalizing the denominator is the process of eliminating radicals from the denominator of a fraction by multiplying numerator and denominator by a suitable radical expression. This makes the expression easier to interpret and work with.

Properties of Square Roots

The properties of square roots include rules such as √a * √b = √(ab) and (√a)^2 = a. These properties help in manipulating and simplifying expressions involving square roots, especially when performing operations like multiplication or division.