The area of a square graden is 173 square feet. Estimate the side lenght of the garden.

Answer 1

To estimate the square root of 173, we determine that 173 is a little more than 169 (13*13) and less than 196 (14*14). This is why you learn the values of the squares of integers.

number square

---------- ---------

0 0

1 1

2 4

. . . . . .

10 100

11 121

12 144

13 169

14 196

15 225

16 256

... ...

Using similar logic, we estimate that the square root of 200 is a little more that 14. It is actually 14.14. This becomes very interesting when you realize that the square root of 2 is 1.414.

Square root of 100 ia 10 Use 1 00

Square root of 10000 is 100 Use 1 00 00

Square root of 1000000 is 1000. Use 1 00 00 00

...

So, we can separate the number pairs of digits and estimate the square root.

What is the square root of 900?

9 00

3 0 The square root of 900 is 30.

Answer 2

Since the garden is a square, the area will be determined by multiplying the side measurement by the side measurement. If we use the variable s to represent the measurement of the side of the square, then we can write the following equation for the area (A): A = s * s or s^2

A = s^2

Since the area is 173 square feet, we can write:

173 = s^2

s will be the square root of 173 which is approximately equal to 13.15 feet.

(13.15 * 13.15 = 172.92)