Using a number line, what is the approximate value of 19−−√?(1 point)

Question

Responses

4.25
4.25

4.38
4.38

4.13
4.13

4.5

Answer 1

To approximate the value of \( \sqrt{19} \) using a number line, we can check the squares of numbers around it.

We know:

• \( 4^2 = 16 \)
• \( 5^2 = 25 \)

This tells us that \( 4 < \sqrt{19} < 5 \).

Next, we can narrow it down further by checking more numbers:

• \( 4.3^2 = 18.49 \)
• \( 4.4^2 = 19.36 \)

Since \( 18.49 < 19 < 19.36 \), we can see that:

• \( 4.3 < \sqrt{19} < 4.4 \)

For more precision, we can try \( 4.35 \):

• \( 4.35^2 = 18.9225 \)

Since \( 18.9225 < 19 \), we have:

• \( 4.35 < \sqrt{19} < 4.4 \)

Estimating more closely, we find that \( \sqrt{19} \) is approximately \( 4.36 \).

Among the given options, the closest approximate value to \( \sqrt{19} \) would be 4.38.

Answer 2

Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses

between 10.5 and 11
between 10.5 and 11

between 9.5 and 10
between 9.5 and 10

between 10 and 10.5
between 10 and 10.5

between 11 and 11.5

Answer 3

To find the approximate value of \( \sqrt{105} \) using a number line, we first identify the square numbers around it.

• \( 10^2 = 100 \)
• \( 11^2 = 121 \)

From this, we know that: \[ 10 < \sqrt{105} < 11 \]

Next, we can narrow it down further:

Calculating \( 10.5^2 \): \[ 10.5^2 = 110.25 \]

Since \( 110.25 > 105 \), we can see that: \[ \sqrt{105} < 10.5 \]

Now calculating \( 10.25^2 \): \[ 10.25^2 = 105.0625 \]

Since \( 105.0625 > 105 \), this shows that: \[ \sqrt{105} < 10.25 < 10.5 \]

Calculating \( 10.2^2 \): \[ 10.2^2 = 104.04 \]

Since \( 104.04 < 105 \), we have: \[ 10.2 < \sqrt{105} < 10.25 \]

Thus, \( \sqrt{105} \) is approximately between 10.2 and 10.25.

This places \( \sqrt{105} \) between the whole number 10 and the rational number 10.5.

Therefore, the answer is: between 10 and 10.5.

Answer 4

Using rational approximations, what statement is true?(1 point)
Responses

48−−√>36−−√
start root 48 end root greater than start root 36 end root

48−−√<36−−√
start root 48 end root less than start root 36 end root

49−−√<7
start root 49 end root less than 7

49−−√>7

Answer 5

Let’s analyze each of the statements one by one to determine which one is true.

1. \( \sqrt{48} > \sqrt{36} \):

   • \( \sqrt{36} = 6 \)
   • \( \sqrt{48} \) is approximately \( 6.928 \) (since \( 6.928^2 \) is close to 48).
   • Thus, \( \sqrt{48} > \sqrt{36} \) is true.

2. \( \sqrt{48} < \sqrt{36} \):

   • Since we've established \( \sqrt{48} > \sqrt{36} \), this statement is false.

3. \( \sqrt{49} < 7 \):

   • \( \sqrt{49} = 7 \).
   • Therefore, this statement is false because \( \sqrt{49} \) is equal to 7, not less than it.

4. \( \sqrt{49} > 7 \):

   • Again, since \( \sqrt{49} = 7 \), this statement is false.

Given these evaluations, the true statement is: \( \sqrt{48} > \sqrt{36} \).

Answer 6

Using rational approximations, what statement is true?(1 point)
Responses

81−−√>9
start root 81 end root greater than 9

71−−√>61−−√
start root 71 end root greater than start root 61 end root

81−−√<9
start root 81 end root less than 9

71 −−−√<61−−√

Answer 7

Let's evaluate each statement one by one:

1. \( \sqrt{81} > 9 \):

   • \( \sqrt{81} = 9 \).
   • Therefore, this statement is false because \( \sqrt{81} \) is equal to 9, not greater than it.

2. \( \sqrt{71} > \sqrt{61} \):

   • To compare, we can find approximate values:
     • \( \sqrt{71} \) is approximately \( 8.43 \) (since \( 8.43^2 \) is around 71).
     • \( \sqrt{61} \) is approximately \( 7.81 \) (since \( 7.81^2 \) is around 61).
   • Thus, \( \sqrt{71} > \sqrt{61} \) is true.

3. \( \sqrt{81} < 9 \):

   • As noted before, \( \sqrt{81} = 9 \).
   • Therefore, this statement is false.

4. \( \sqrt{71} < \sqrt{61} \):

   • Since we've established that \( \sqrt{71} > \sqrt{61} \), this statement is false.

Among the options, the true statement is: \( \sqrt{71} > \sqrt{61} \).

Answer 8

A company makes hanging ornaments in various shapes. The heights of the ornaments are shown. Using a calculator, order these ornaments from tallest to shortest.

(1 point)
Responses

square, diamond, triangle
square, diamond, triangle

square, triangle, diamond
square, triangle, diamond

diamond, square, triangle
diamond, square, triangle

triangle, square, diamond

Answer 9

To accurately order the ornaments from tallest to shortest, we would need the actual heights of the square, diamond, and triangle ornaments. Since these heights are not provided in your message, I cannot determine the correct order.

If you have the heights of the ornaments, please provide that information, and I'd be happy to assist in ordering them. If you're looking for assistance with understanding how to approach this task, here’s a general method:

1. List the heights of each ornament.
2. Compare the heights.
3. Order them from tallest to shortest based on their measured values.

If you provide the heights, I can help further!