Question
Vocabulary Terms - Define/Illustrate
Interpreting Irrational answers for side lengths of squares and cubes.
Interpreting Irrational answers for time and money
5 Problems - SHOW ALL WORK!
If you solve a problem with a formula and you get the answer √ 20 minutes. How long is that?
If a square room has a floor with an area of 289 square feet, how long is each side of the floor?
If a cube has a volume of 1,750 mm^3 feet, how long is each side of the cube?
If you apply a formula and your answer is $√65 . How much money is that?
Xander plans to raise hogs. He builds a pig pen 23’ x 32’ and knows that each pig requires about 6 ft.^2 space. How many pigs can he fit in the pen?
Interpreting Irrational answers for side lengths of squares and cubes.
Interpreting Irrational answers for time and money
5 Problems - SHOW ALL WORK!
If you solve a problem with a formula and you get the answer √ 20 minutes. How long is that?
If a square room has a floor with an area of 289 square feet, how long is each side of the floor?
If a cube has a volume of 1,750 mm^3 feet, how long is each side of the cube?
If you apply a formula and your answer is $√65 . How much money is that?
Xander plans to raise hogs. He builds a pig pen 23’ x 32’ and knows that each pig requires about 6 ft.^2 space. How many pigs can he fit in the pen?
Answers
Answer
what about 4 and 5 and the definitions/illustrate
Answered by
GPT-4o mini
Let's break down and solve each problem step by step, paying attention to the irrational answers and how to interpret them.
### Problem 1: Time Calculation
**If you solve a problem with a formula and you get the answer √20 minutes. How long is that?**
To find out what √20 minutes is:
1. Calculate √20.
\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]
2. Now calculating √5 (approximate value):
\[
\sqrt{5} \approx 2.236
\]
Therefore,
\[
2\sqrt{5} \approx 2 \times 2.236 \approx 4.472
\]
3. So, √20 minutes is approximately 4.472 minutes.
### Problem 2: Area of a Square Room
**If a square room has a floor with an area of 289 square feet, how long is each side of the floor?**
The area (A) of a square is given by the formula:
\[
A = s^2
\]
Where \(s\) is the side length of the square. To find the side length:
1. Set the area equal to 289:
\[
s^2 = 289
\]
2. Take the square root of both sides:
\[
s = \sqrt{289} = 17
\]
Therefore, each side of the floor is **17 feet**.
### Problem 3: Volume of a Cube
**If a cube has a volume of 1,750 mm³, how long is each side of the cube?**
The volume (V) of a cube is given by the formula:
\[
V = s^3
\]
Where \(s\) is the side length of the cube. To find the side length:
1. Set the volume equal to 1,750:
\[
s^3 = 1750
\]
2. Take the cube root of both sides:
\[
s = \sqrt[3]{1750}
\]
To find this value:
\[
s \approx 12.145
\]
Thus, each side of the cube is approximately **12.145 mm**.
### Problem 4: Money Calculation
### Problem 1: Time Calculation
**If you solve a problem with a formula and you get the answer √20 minutes. How long is that?**
To find out what √20 minutes is:
1. Calculate √20.
\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]
2. Now calculating √5 (approximate value):
\[
\sqrt{5} \approx 2.236
\]
Therefore,
\[
2\sqrt{5} \approx 2 \times 2.236 \approx 4.472
\]
3. So, √20 minutes is approximately 4.472 minutes.
### Problem 2: Area of a Square Room
**If a square room has a floor with an area of 289 square feet, how long is each side of the floor?**
The area (A) of a square is given by the formula:
\[
A = s^2
\]
Where \(s\) is the side length of the square. To find the side length:
1. Set the area equal to 289:
\[
s^2 = 289
\]
2. Take the square root of both sides:
\[
s = \sqrt{289} = 17
\]
Therefore, each side of the floor is **17 feet**.
### Problem 3: Volume of a Cube
**If a cube has a volume of 1,750 mm³, how long is each side of the cube?**
The volume (V) of a cube is given by the formula:
\[
V = s^3
\]
Where \(s\) is the side length of the cube. To find the side length:
1. Set the volume equal to 1,750:
\[
s^3 = 1750
\]
2. Take the cube root of both sides:
\[
s = \sqrt[3]{1750}
\]
To find this value:
\[
s \approx 12.145
\]
Thus, each side of the cube is approximately **12.145 mm**.
### Problem 4: Money Calculation