College Algebra by OpenStax

By OpenStax

University Algebra offers a complete and multi-layered exploration of algebraic ideas. The textual content is acceptable for a standard introductory Algebra path, and used to be built for use flexibly. The modular technique and the richness of content material guarantees that the ebook meets the desires of quite a few courses. collage Algebra publications and helps scholars with differing degrees of guidance and adventure with arithmetic. principles are provided as basically as attainable, and development to extra complicated understandings with significant reinforcement alongside the best way. A wealth of examples - often numerous dozen consistent with bankruptcy - provide precise, conceptual factors, which will construct in scholars a robust, cumulative beginning within the fabric prior to asking them to use what they have discovered. this can be a full-color textbook.

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147k3 ​ — — 58. ​ ​ _ 2 ​ ​ 3 — 3 — 60. √ ​ 24x6 ​ + ​ √ 81x6 ​ 3 — 63. √ ​ 128z3 ​ − ​ √ −16z3 ​ 4 — 6 162x _____ ​ ​ ​ √ 16x 61. ​ 3 — 62. √ ​ 64y ​ 4 5 — 64. √ ​ 1,024c10 ​ REAL-WORLD APPLICATIONS 65. A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet.

Since 23 = 8, we say that 2 is the cube root of 8. The nth root of a is a number that, when raised to the nth power, gives a. For example, −3 is the 5th root of −243 because (−3)5 = −243. If a is a real number with at least one nth root, then the principal nth root of a is the number with the same sign as a that, when raised to the nth power, equals a. n — The principal nth root of a is written as √ ​ a ​ , where n is a positive integer greater than or equal to 2. In the radical expression, n is called the index of the radical.

26x7y ​ 11 Solution _______ √ 234x11y ​ ​ Combine numerator and denominator into one radical expression. ​ ______ ​ 26x7y — Simplify fraction. ​ √ 9x4 ​ 3x 2 Try It #5 Simplify square root. — ​ 9a5 b 14 ​ √ ​ . Simplify ________ ​ — ​ 3a4b5 ​ √ Adding and Subtracting Square Roots We can add or subtract radical expressions only when they have the same radicand and when they have the same — — — radical type such as square roots. For example, the sum of ​√ 2 ​ and 3​√ 2 ​ is 4​√ 2 ​ . However, it is often possible to — simplify radical expressions, and that may change the radicand.

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