10.11 摘要:根和激进功能
章节大纲
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In this chapter, we learned:
::在本章中,我们学到:How to Evaluate nth Roots
::如何评估 nth 根-
Find a number that multiplied by itself the number of times in the index that is the radicand. It is helpful to find the prime factorization of the number to do this.
::查找一个自动乘以索引中值为弧形的乘数。 找到数字的质因数来做这个计算很有帮助 。 -
Use the properties of radicals to separate radicals of products or quotients, and take a root 1st and then apply a power, or vice versa.
::利用激进分子的特性来分离产品或商数的激进分子,然后从头开始,然后运用权力,反之亦然。
How to Evaluate Rational Exponents
::如何评价有理人才-
Note that rational exponents of the form
correspond to roots of the form
.
::请注意窗体 a1n 的理性引言与窗体 an 的根对应。 -
To evaluate rational exponents, use the power rule of exponents to take the root and then apply the integer exponent.
::为了评估理性指数,使用指数规则根根,然后应用整数指数。 -
To rationalize a denominator with one term, multiply the numerator and the denominator by the radical the number of times in the index.
::要合理使用一个术语来理顺一个分母,将分子和分母乘以指数中的极端次数。 -
To rationalize a denominator with two terms, multiply by the conjugate.
::用两个词来理顺一个分母 乘以同义词 -
Remember that the laws of exponents—particularly the product, quotient, and power rules—apply to rational exponents as well.
::记得先行者的法律——特别是产品、商数和权力规则——也适用于理性先行者。
How to Solve Radical Equations
::如何解决激进等同-
To solve a radical equation, isolate the radical expression, use the power rule to undo the radical, solve the equation, and check for extraneous solutions.
::为了解决激进方程式, 孤立激进表达, 使用权力规则推翻激进, 解决方程式, 并检查不相干的解决办法。 -
To solve rational equations with variables on both sides, isolate one radical expression at a time and follow the steps as in the previous bullet.
::要用两边变量解决理性方程式, 一次孤立一个激进表达式, 并遵循前一个圆点的步骤 。
How to Graph Square and Cube Root Functions
::如何图形平方和立方根函数-
To graph a square root function, determine the domain, choose 3 to 5 values in the domain for a table of values, plot them, and draw the graph.
::要绘制平方根函数图,确定域,在域中选择 3 至 5 个数值以图示数值表,绘制它们,并绘制图表。 -
To graph cube root functions, make a table of values, plot the points, and graph the function.
::要绘制 立方体 根 函数,请绘制一个数值表,绘制点图,并绘制函数图。
Looking Back, Looking Forward
::回顾,展望未来In this chapter, we expanded our knowledge of radical expressions. We learned how to evaluate higher-index roots, solve equations with radicals, and graph radical functions. This allowed us to approach applications like crashes in video games, the surface area of the human body, and tsunamis.
::在本章中,我们扩展了对激进表达方式的知识。我们学会了如何评估高指数根,用激进元素解析方程式,以及图形激进函数。这使我们能够使用电玩撞车、人体表面面积和海啸等应用程序。We also learned about rational exponents, and in the next chapter we'll consider exponents more by looking at exponential and logarithmic functions.
::我们还了解了理性的推论者, 在下一章中,我们将考虑更多的推论者 通过查看指数函数和对数函数。Chapter Review
::回顾章次审查 -
Find a number that multiplied by itself the number of times in the index that is the radicand. It is helpful to find the prime factorization of the number to do this.