Question

1. calculate each square root to one decimal place. choose one of your answers and explain why it is reasonable.

a) √18 c) √38 e) √800
b) √75 d) √150 f) √3900

1. a square field has an area of 3000 m².

a) explain how you can use √3000 to estimate the side length of the square.
b) how do you know the side length is between 50 m and 60 m?
c) calculate the side length of the square field. round your answer to one decimal place.

1. what can you add to each number to make a perfect square?

a) 42 b) 101 c) 399 d) 875

1. tiananmen square in beijing, china, is the largest open “square” in any city in the world. it is actually a rectangle of 880 m by 500 m.

a) what would be the approximate side length of a square with the same area as tiananmen square?
b) explain how you know your answer is reasonable.

Explanation:

5a.

Step1: Find two perfect - squares around 18

We know that $4^2 = 16$ and $5^2=25$.

Step2: Estimate the square - root

Since 18 is closer to 16 than 25, $\sqrt{18}\approx4.2$.

5b.

Step1: Find two perfect - squares around 75

We know that $8^2 = 64$ and $9^2 = 81$.

Step2: Estimate the square - root

Since 75 is closer to 81 than 64, $\sqrt{75}\approx8.7$.

5c.

Step1: Find two perfect - squares around 38

We know that $6^2 = 36$ and $7^2 = 49$.

Step2: Estimate the square - root

Since 38 is closer to 36 than 49, $\sqrt{38}\approx6.2$.

5d.

Answer:

Step1: Calculate the area of Tiananmen Square

The area of Tiananmen Square $A=880\times500 = 440000$ m².

Step2: Find the side - length of a square with the same area

Let the side - length of the square be $s$. Then $s=\sqrt{440000}=663.4$ m (rounded to one decimal place).

8b.

We know that $600^2=360000$ and $700^2 = 490000$. Since $360000<440000<490000$, the side - length of the square with area 440000 m² is between 600 m and 700 m. And 663.4 m is in this range, so the answer is reasonable.