1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
laiz [17]
1 year ago
8

What does it mean to determine the two positive integers that each value is between??? I'm confused ​

Mathematics
1 answer:
KIM [24]1 year ago
7 0

Answer:

  11. {7, 8}

  12. {8, 9}

  13. {8, 9}

  14. {4, 5}

Step-by-step explanation:

You want consecutive integers that bracket each of the given irrational roots.

<h3>Square roots</h3>

A square root of an integer will be rational only if the integer is a perfect square. The first few perfect squares are ...

  • 1² = 1
  • 2² = 4
  • 3² = 9
  • 4² = 16
  • 5² = 25
  • 6² = 36
  • 7² = 49
  • 8² = 64
  • 9² = 81

You know these because you know your multiplication tables.

The square root of a number between these perfect squares will lie between the roots of the squares.

<h3>11. √50</h3>

50 lies between the squares 49 = 7² and 64 = 8². That means √50 lies between 7 and 8.

Your calculator tells you that √50 ≈ 7.0710678, which is a number that lies between the integers 7 and 8.

<h3>12. √72</h3>

72 lies between the squares 64 = 8² and 81 = 9². That means √72 lies between 8 and 9.

<h3>13. √65</h3>

65 lies between the squares 64 = 8² and 91 = 9². That means √65 lies between 8 and 9.

<h3>14. √23</h3>

23 lies between the squares 16 = 4² and 25 = 5². That means √23 lies between 4 and 5.

__

<em>Additional comment</em>

The purpose of questions like this appears to be to have you make use of your knowledge of integer perfect squares to guess an approximation of a square root.

A calculator can answer these questions immediately. Of course the two consecutive integers are the integer part of the root, and the next higher integer.

The question is not well-posed. The answer to "integers each value is between" could be 1 < √50 < 50. For integers greater than 1, the square root is always smaller than the integer being rooted. We've seen questions like this enough times that we can guess the intention is for you to identify <em>consecutive</em> integers.

<em>Extra credit</em>

Knowing the integer part of the root and the difference between the number and its next lower perfect square, you can approximate the root as follows:

For integer n = a² +b, the root √n lies between a +b/(2a+1) and a +b/(2a).

For example, 65 = 8²+1, so √65 lies between 8 1/17 and 8 1/16.

You might be interested in
A candy box company places an average of 20 truffles in a one pound box. The number of truffles per box never varies from the av
storchak [24]
(x-20) 2
that is the answer

7 0
3 years ago
Joe decides to take his six year old son to the planetarium. The price for the child's ticket is 5.75 dollars less than the pric
Anna007 [38]
Okay, we know the price of the child's ticket (x), which is 5.75 dollars less than the adult's ticket.
Let's say that the price of the adult's ticket is a. Since the child's ticket is 5.75 less that the adult's ticket, we can write it this way:
a = 5.75 + x
6 0
2 years ago
Read 2 more answers
(HELP ASAP)
wariber [46]

Answer:

45 km^2 (C)

Step-by-step explanation:

Isolate the smaller square -

We only need two side lengths, take 3km and 3km.

3×3 = 9km^2, that's the area of the smaller square.

Isolate the larger square -

Take 6km and the other 6km

6×6 = 36km^2

Add the square's areas together to get the whole area -

36 + 9 = 45km^2

All you need to do to solve these problems is to isolate the shapes and find their area's, and finally add them together.

8 0
3 years ago
At the end of a snow storm, Caroline saw there was a lot of snow on her front lawn. The temperature increased and the snow began
valkas [14]

Answer:

-15

Step-by-step explanation:

5 0
3 years ago
Evaluate the expression
Veseljchak [2.6K]

Answer:

3rd Option: 1

Step-by-step explanation:

Step 1: Define

(x + 4)/3x

x = 2

Step 2: Substitute and Evaluate

(2 + 4)/3(2)

6/6

1

6 0
2 years ago
Read 2 more answers
Other questions:
  • What does 3.33333333333 mean in fractions?
    13·1 answer
  • Please I need help. Don’t understand
    12·1 answer
  • How do I solve two-step equations<br><br> ex. 3g+5=17
    10·2 answers
  • if a rectangle has a perimeter of 70, a length of x and a width of x-9, find the value of the length of the rectangle. A)4, B)31
    11·2 answers
  • Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent
    9·1 answer
  • Find the value of x.<br> 30 <br> 17
    9·1 answer
  • How many triples of three positive integers have a product of 16?
    14·1 answer
  • Write 4716 in scientific notation.
    10·1 answer
  • Which is the following is an incorrect way to label the line in the diagram below?​
    8·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Clarge%20%5Crm%20%5Csum%20%5Climits_%7Bn%20%3D%200%7D%5E%20%5Cinfty%20%20%20%5Cfrac%7B%28%20
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!