9.2 对完美广场根的评估

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  完美广场根评价

  

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  Miguel was helping his little brother, Luis, cut several sheets of paper into 4 squares each. The sheets measure 9 inches x 9 inches. Luis insisted that all the squares be "perfect." This reminded Miguel of a math lesson on the difference between "perfectly square," and "perfect squares." Luis wanted cut outs that were "perfectly square." Miguel's homework involved "perfect squares." Do you know the difference?
  ::Miguel帮助他的弟弟Luis, 将几张纸切成4平方。 床单用9英寸乘9英寸乘9英寸。 Luis坚持所有广场都要“ 完美 ” 。 这提醒了Miguel关于“ 完美的正方形” 和“ 完美的正方形” 之间的差别的数学课。 Luis想要切出“ 完美的正方形” 。 Miguel的作业涉及“完美的正方形 ” 。 你知道区别吗?

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  In this concept, you will learn about perfect square roots.
  ::在这个概念中,你会学会完美的平方根。

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  Evaluating Perfect Square Roots
  ::评估完美广场根

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  A  square has four equal sides, meaning it is "perfectly square." This means it is not a rectangle or a parallelogram or any other 4-sided figure. 
  ::方形有四面相等, 意思是“ 完全正方形 ” 。 这意味着它不是一个矩形或平行图, 或任何其他四面图 。

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  If you know the side lengths of a square and want to find the area, you simply "square" the sides.
  ::如果你知道方形的侧边长度 想要找到这个区域, 你只需“平方”两边。

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  $\begin{array}{r}A=s^2\end{array}$
  ::A=s2 阿=2

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  The square root is the opposite calculation. If you know the area of the square and want to find the sides, you determine the root by using your knowledge of the multiplication tables.
  ::平方根是相反的计算方法。如果您知道正方块的面积并想要找到两边,则使用对乘法表格的知识来确定根。

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  $\begin{array}{r}s=\sqrt{A}\end{array}$
  ::=A =A =A

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  A square root is the number that, times itself, produces a given number. Perfect squares are numbers whose square roots are whole numbers .
  ::平方根是乘以本身产生给定数字的数字。完美的平方是平方根为整数的数字。

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  These numbers are perfect squares: 4, 9, 16, 25, 36
  ::这些数字是完美的方形: 4,9,16,25,36

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  When you look at their images, you can see why.
  ::当你看着他们的图像时,你可以看到原因。

  

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  These numbers are perfect squares because their square roots are whole numbers.
  ::这些数字是完美的平方,因为它们的平方根是整数。

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  Let’s examine one.
  ::让我们来检查一下。

    $\begin{array}{r}\sqrt{16}=\end{array}$

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  First, you know that 4 x 4 equals 16.
  ::首先,你知道4x4等于16吗?

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  The answer is 4.
  ::答案是4。

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  4 is the square root of 16, and because 4 is a whole number, we say that 16 is a perfect square.
  ::4是16的平方根,4是整数,我们说16是一个完美的平方。

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  Perfect squares have the easiest square roots to find because they are whole numbers. Most numbers are not perfect squares.
  ::完美的正方块有最容易找到的正方根,因为它们是整数。大多数数字不是完美的正方块。

  

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  What is the square root of 5?
  ::5的平方根是什么?

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  First, the diagram shows that 4, 5, and 9 are all "perfectly square," meaning that in each square, the sides are equal.
  ::首先,图表显示 4,5,9 都是“完全正方形”, 这意味着在每一个正方形, 双方是平等的。

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  Next, the square root of 5 cannot be easily determined because 5 does not appear in the multiplication tables. You cannot easily identify a number to multiply times itself to get 5 as the answer. 
  ::其次,5的平方根无法轻易确定, 因为 5 没有出现在乘法表格中 。 您无法轻易识别乘以乘以乘以本身的数, 以获得 5 作为答案 。

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  Then, you know that 5 is not a perfect square. Its square root is not a whole number but is somewhere between 2 and 3. It falls between the perfect squares of 4 and 9. 
  ::那么,你知道,5不是一个完美的平方。它的平方根不是一个完整的数字,而是介于2到3之间。它位于4到9的完美平方之间。

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  Next, using a calculator, you can solve the equation.
  ::接下来,使用计算器,你可以解析方程式。

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  The answer is $\begin{array}{r}\sqrt{5}\end{array}$ is roughly 2.236067978
  ::答案是5,大约是2,2306778

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  That is definitely not a perfect square! But your estimate of between 2 and 3 was correct.
  ::这绝对不是一个完美的广场! 但你对2到3之间的估计是正确的。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about  Miguel and Luis, who are cutting squares.
  ::早些时候,你被问及米格尔和路易斯的问题,他们正在切割方块。

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  If the boys are using paper that measures 9 inches by 9 inches and are cutting it into four pieces, are they cutting perfect squares or just pieces that are perfectly square?
  ::如果男孩们用纸,用9英寸乘9英寸,然后把它切成四块, 是切割完美的正方形还是完全正方形?

  

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  First, since the sheets of paper measure 9 inches x 9 inches, and 9 is a whole number, you know that  $\begin{array}{r}{9}^2=81\end{array}$ and 81 is a perfect square. The uncut sheets are perfect squares.
  ::首先,由于纸面表的尺寸是9英寸x9英寸,9英寸是一个整数, 你知道92=81和81是一个完美的正方形。未剪切的平面是完美的正方形。

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  Next, when the paper is cut into four squares, each smaller square has sides that measure 4.5 inches x 4.5 inches.
  ::接下来,当纸切成四个方形时,每个较小方形的两边都有4.5英寸x4.5英寸的尺寸。

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  Then, since 4.5 is not a whole number, Luis's cut outs are not perfect squares.
  ::既然4.5并不是一个完整的数字, 路易斯的切出不是完美的方形。

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  The answer is that Luis's squares are perfectly square, but they are not perfect squares. 
  ::答案是路易斯的方块完全正方形 但并不是完美的方块

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  Example 2
  ::例2

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  Is 169 a perfect square? 
  ::169是个完美的广场吗?

    $\begin{array}{r}\sqrt{169}\end{array}$

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  First, think about what number times itself could be equal to 169.
  ::首先,考虑一下多少倍本身可以等于169倍。

    $\begin{array}{r}12\times 12=144\end{array}$

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  Next, let's try 13.
  ::接下来,让我们尝试13。

    $\begin{array}{r}13\times 13=169\end{array}$

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  The answer is 13. The square root of 169 is 13. Since 13 is a whole number, 169 is a perfect square.
  ::答案是13,169的平方根是13,因为13是一个整数,169是一个完美的平方。

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  Find the following square roots and identify the perfect squares.
  
  ::找到以下的平方根 并识别完美的平方。

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  Example 3
  ::例3

    $\begin{array}{r}\sqrt{121}\end{array}$

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  First, think of what number times itself might equal 121.
  ::首先,想想多少倍本身可能等于121倍。

    $\begin{array}{r}10\times 10=100\end{array}$

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  Next, try 11.
  ::下一个,试试11

    $\begin{array}{r}11\times 11=121\end{array}$

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  The answer is 11 . The square root of 121 equals 11. Since 11 is a whole number, 121 is a perfect square.
  ::答案是11 121的平方根等于11 由于11是整数 121是完美的平方

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  Example 4
  ::例4

    $\begin{array}{r}\sqrt{74}\end{array}$

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  First, think of the multiplication tables.
  ::首先,想想乘法表。

    $\begin{array}{r}8\times 8=64\end{array}$

    $\begin{array}{r}9\times 9=81\end{array}$

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  Next, 74 lies somewhere between 64 and 81.
  ::接下来,74个位于64到81之间。

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  Then, $\begin{array}{r}\sqrt{74}\end{array}$ lies somewhere between 8 and 9.
  ::然后,74在8到9之间。

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  Use a calculator and round your answer to one decimal.
  ::使用计算器,然后将回答转至小数点后一位。

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  The answer is 8.6 and this root is not a whole number. 74 is not a perfect square.
  ::答案是8.6,这个根不是完整的数字。 74不是一个完美的正方形。

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  Example 5
  ::例5

    $\begin{array}{r}\sqrt{40}\end{array}$

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  First, think of the perfect squares you know.
  ::首先,想想你知道的完美的方形

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  6 x 6 = 36
  ::6x6=36

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  7 x 7 = 49
  ::7 x 7 = 49

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  Then, 40 is not a perfect square.
  ::那么,40不是一个完美的广场。

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  The answer is $\begin{array}{r}\sqrt{40}\end{array}$ is somewhere between 6 and 7. You can use a calculator to find the exact root.
  ::答案是40,大约在6到7之间, 你可以使用计算器找到确切的根。

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  Review
  ::回顾

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  Evaluate each square root.
  ::评估每一平方根。

  1. $\begin{array}{r}\sqrt{36}\end{array}$
  2. $\begin{array}{r}\sqrt{49}\end{array}$
  3. $\begin{array}{r}\sqrt{64}\end{array}$
  4. $\begin{array}{r}\sqrt{81}\end{array}$
  5. $\begin{array}{r}\sqrt{100}\end{array}$
  6. $\begin{array}{r}\sqrt{121}\end{array}$
  7. $\begin{array}{r}\sqrt{144}\end{array}$
  8. $\begin{array}{r}\sqrt{196}\end{array}$
  9. $\begin{array}{r}\sqrt{400}\end{array}$
  10. $\begin{array}{r}\sqrt{900}\end{array}$
  11. $\begin{array}{r}\sqrt{10000}\end{array}$
  12. $\begin{array}{r}\sqrt{225}\end{array}$
  13. $\begin{array}{r}\sqrt{256}\end{array}$
  14. $\begin{array}{r}\sqrt{324}\end{array}$
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  15. What do all of these square roots have in common?
      ::所有这些平方根有什么共同之处?

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源