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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. P - Fundamental Concepts of Algebra문제 47
1장, 문제 47

Rationalize the denominator.
25\(\frac{\sqrt{2}\)}{\(\sqrt{5}\)}

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1
Identify the expression to rationalize: \(\frac{\sqrt{2}}{\sqrt{5}}\). The goal is to eliminate the square root from the denominator.
Multiply both the numerator and the denominator by \(\sqrt{5}\), which is the conjugate in this case, to rationalize the denominator. This gives: \(\frac{\sqrt{2}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}\).
Use the property of square roots that \(\sqrt{a} \times \sqrt{a} = a\) to simplify the denominator: \(\sqrt{5} \times \sqrt{5} = 5\).
Multiply the numerators together: \(\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} = \sqrt{10}\).
Write the new expression with the rationalized denominator: \(\frac{\sqrt{10}}{5}\). This is the simplified form with no radical in the denominator.

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주요 개념

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

Rationalizing the Denominator

Rationalizing the denominator involves eliminating any radicals (square roots) from the denominator of a fraction. This is done by multiplying the numerator and denominator by a suitable expression that will remove the radical from the denominator, making the expression easier to interpret and use.
추천 영상:
02:58
Rationalizing Denominators

Properties of Square Roots

Square roots have properties such as \( \sqrt{a} \times \sqrt{b} = \sqrt{ab} \) and \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \). Understanding these properties helps simplify expressions involving radicals and is essential when rationalizing denominators.
추천 영상:
02:20
Imaginary Roots with the Square Root Property

Multiplying by a Form of One

To rationalize a denominator, multiply the fraction by a form of one that contains the radical in the denominator, such as \( \frac{\sqrt{5}}{\sqrt{5}} \). This does not change the value of the expression but helps eliminate the radical from the denominator.
추천 영상:
04:15
Multiply Polynomials Using the Distributive Property
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