课程： 9.1 对 " 平根 " 的评价 | The Way To Learn

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平根评价
Brittany is replacing the old tiles on a small tabletop for her mom's upcoming birthday. The area that needs to be covered is 64 square inches, so Brittany bought new 1-inch square tiles. How many rows of tiles will she need to cover the table? How many tiles will be in each row?
::布列塔尼正在更换一张小桌子上的旧瓷砖,为她妈妈即将到来的生日。需要覆盖的面积是64平方英寸,所以布列塔尼买了新的1英寸方格瓷砖。她需要多少排瓷砖才能覆盖桌子? 每排有多少张瓷砖?

In this concept, you will learn what a square root is and how to find it.
::在这个概念中,你会知道什么是平方根以及如何找到它。

Evaluating Square Roots
::评估广场根

A square is a unique shape in that all four sides are equal in length.
::方形是一个独特的形状,四面的长度相等。

In order to find the area of the square (the number of units it covers), you can "square" one side.
::为了找到方形的区域( 其覆盖的单位数), 您可以“ 平方” 一面。

$\begin{aligned} A = s^{2} \end{aligned}$

::A=s2 阿=2

To " square " a number means to multiply it by itself.
::"平方"的数数意味着它本身的乘数。

This type of calculation requires multiplying the parts (side lengths) in order to find the whole (area).
::这种类型的计算要求各部分(外长)乘以乘以,才能找到整个(区域)。

Let's look at an example.
::让我们举个例子。

If you have a square with 6" sides, you multiply 6" x 6", or $\begin{aligned} 6^{2} \end{aligned}$ , to get an area of 36 square inches (Don't forget that when you multiply the units of inches, they also get squared . Your answer is not inches, but rather inches squared.)
::如果您有一个有 6 边的方形, 乘 6" x 6" 或 62, 以获得36 平方英寸的区域( 不要忘记, 当您乘乘英寸时, 单位的单位也会得到平方。您的回答不是英寸, 而是英寸的平方。 )

This is the symbol used to find the square root of x. $\begin{aligned} \sqrt{x} \end{aligned}$
::这是用来查找 x. x 平方根的符号

A square root is a part that when you multiply it by itself (the other part) equals the whole.The root of a square is one of its parts (the length of one side). Finding the "root" of a square is the opposite calculation of squaring. In order to find it, you will be given the whole (the area), and you will need to find the parts. The good news is that the parts in a square are always equal!
::平方根是一个部分, 当您将平方根本身乘以来( 另一部分) 等于整块时。平方根是其中的一个部分( 一方的长度 ) 。找到平方的“ 根” 是相反的对角计算。要找到平方根, 要找到平方根, 就需要将整块( 面积) 给您, 并且需要找到整块。好消息是, 平方各部分总是相等。

All numbers have a square root, even those that are not perfect squares. A perfect square is a number for which the roots are whole numbers . These are found in your multiplication tables.
::所有数字都有平方根, 即使那些不是完美的正方根。完美的正方是一个数字, 根是整数。这些都在您的乘法表格中。

All positive numbers also have a negative square root. Remember that when you multiply a negative number times a negative number, the answer is a positive . Positive numbers will have both a positive and negative root of the same absolute value.
::所有正数都有负平方根。记住, 当负数乘以负数乘以负数时, 答案是正数。正数将具有相同绝对值的正数和负数根。

Let's look at some more examples.
::让我们再举几个例子。

$\begin{aligned} \sqrt{16} = 4 \end{aligned}$

The root, 4, is a whole number. Therefore, the number 16 is a perfect square.
::根,4是一个整数。因此,16是一个完美的正方形。

$\begin{aligned} \sqrt{25} = 5 \end{aligned}$

The number 25 is a perfect square.
::25号是完美的正方形

$\begin{aligned} \sqrt{20} = 4.47 \end{aligned}$

This is a decimal root. The number 20 is NOT a perfect square. Its root is somewhere between the whole numbers of 4 and 5.
::这是小数点根。数字 20 不是完美的正方形。其根在 4 和 5 之间。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Brittany and the tiles for her table.
::早些时候,你得到一个问题关于布列塔尼和瓷砖为她的桌子。

She has 1" square tiles and needs to cover the 64 square inch table top. How many tiles will be in each row, and how many rows does she need?
::她有1平方瓦,需要覆盖64平方英寸的表顶。每行有多少瓦,她需要多少行?

First, you know that the perfect square $\begin{aligned} 64 = 8 \times 8 \end{aligned}$ , or   $\begin{aligned} 8^{2} \end{aligned}$ .
::首先,你知道,完全正方 64=8x8,或82。

The answer is $\begin{aligned} \sqrt{64} = 8 \end{aligned}$ . Brittany should have 8 rows of tiles with 8 tiles in each row.
::答案是 64=8. 布列塔尼应该有8行瓷砖,每行8张瓷砖。

Example 2
::例2

Find the square root of 9.
::找出9的平方根

First, remember that you are working with a perfect square; all sides are equal.
::首先,要记住,你的工作是一个完美的平方;各方是平等的。

Next, picture that square of 9 units in your mind.
::接下来,想象一下你脑中的9个单元的平方。

Then think, "What number do you multiply by itself (or "square") to get 9?
::然后想,“你乘以多少数字来获得9?”

The answer is 3.
::答案是3

The square root of 9, $\begin{aligned} \sqrt{9} \end{aligned}$ , is 3 because $\begin{aligned} 3^{2} \end{aligned}$ , or $\begin{aligned} 3 \times 3 \end{aligned}$ , is equal to 9.
::平方根为9,9,3,因为32或3x3等于9。

Example 3
::例3

Find   $\begin{aligned} \sqrt{49} \end{aligned}$
::找找49

First, as the numbers get bigger, it may be difficult to picture them in your mind, so think of the perfect squares that appear in your multiplication tables.
::首先,随着数字的扩大, 可能很难在你的脑海中想象它们, 所以想一想在你的乘法表中出现的完美的方形。

Next, ask yourself, "what number times itself equals 49?"
::接下来,你问自己, “自己多少倍等于49?”

$\begin{aligned} 5 \times 5 = 25 \end{aligned}$

$\begin{aligned} 6 \times 6 = 36 \end{aligned}$

Then, $\begin{aligned} 7 \times 7 = 49 \end{aligned}$
::然后,7x7=49

The answer is 7.
::答案是7个

$\begin{aligned} \sqrt{49} = 7 \end{aligned}$

Example 4
::例4

Evaluate $\begin{aligned} \sqrt{21} \end{aligned}$
::评价21

First, the whole number 21 does not appear in your multiplication tables because it is not a perfect square.
::首先,整个数字21没有出现在你的乘法表中, 因为它不是一个完美的平方。

Next, think about the perfect squares it may fall between.
::接下来,考虑一下它可能落在中间的完美的方形。

$\begin{aligned} 4^{2} = 16 \end{aligned}$

$\begin{aligned} 5^{2} = 25 \end{aligned}$

21 is between the perfect squares of 16 and 25.
::21是16到25的完美方形之间

The answer is $\begin{aligned} \sqrt{21} \end{aligned}$ is between 4 and 5.
::答案是21是4到5之间

Example 5
::例5

The YMCA is collecting artwork by children to hang on the wall of their art center. Each submission must cover a square space of 100 square inches. What size sheet of paper should Brent use to paint a self portrait?
::基督教青年会正在收集儿童艺术作品以挂在艺术中心的墙壁上。每份呈文必须覆盖100平方英寸的平方空间。布伦特应该用什么尺寸的纸张来画一张自画像?

First, think about what information is given to you. The drawing must be square, and it must cover 100 square inches. To know the length of the sides, you must find the square root of 100.
::首先, 想想给您的信息。绘图必须是平方的, 并且必须覆盖100平方英寸。要知道两边的长度, 您必须找到100平方英寸的平方根。

Then, think of the perfect squares in your multiplication tables.
::然后想想你乘法表中的完美方形

$\begin{aligned} 9^{2} = 81 \end{aligned}$

$\begin{aligned} 10^{2} = 100 \end{aligned}$

The answer is $\begin{aligned} \sqrt{100} = 10 \end{aligned}$ . Brent needs a sheet of paper that measures 10 inches by 10 inches.
::答案是100=10 布伦特需要一张纸 10英寸乘10英寸

Review
::回顾

Evaluate each square root.
::评估每一平方根。

$\begin{aligned} \sqrt{16} \end{aligned}$

$\begin{aligned} \sqrt{25} \end{aligned}$

$\begin{aligned} \sqrt{1} \end{aligned}$

$\begin{aligned} \sqrt{49} \end{aligned}$

$\begin{aligned} \sqrt{144} \end{aligned}$

$\begin{aligned} \sqrt{81} \end{aligned}$

$\begin{aligned} \sqrt{169} \end{aligned}$

$\begin{aligned} \sqrt{121} \end{aligned}$

$\begin{aligned} \sqrt{100} \end{aligned}$

$\begin{aligned} \sqrt{256} \end{aligned}$

Name the two values each square root is between.
::每个平方根之间列出两个值。

$\begin{aligned} \sqrt{12} \end{aligned}$

$\begin{aligned} \sqrt{14} \end{aligned}$

$\begin{aligned} \sqrt{30} \end{aligned}$

$\begin{aligned} \sqrt{40} \end{aligned}$

$\begin{aligned} \sqrt{50} \end{aligned}$

$\begin{aligned} \sqrt{62} \end{aligned}$

$\begin{aligned} \sqrt{70} \end{aligned}$

$\begin{aligned} \sqrt{101} \end{aligned}$

$\begin{aligned} \sqrt{5} \end{aligned}$

$\begin{aligned} \sqrt{15} \end{aligned}$

Review (Answers)
::回顾(答复)

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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