Start by finding consecutive perfect squares around the value from Part A. Then find the decimal between them, whose square will be the nearest to the number under the root.
A
sqrt(45)
B
Width: 6.7 Length: 13.4
Practice makes perfect
We are given a rectangle that has an area of 90 square units and a length that is twice the width.
As was said, we can divide it into two squares. To do this we will connect the halves of the longer sides of the given rectangle.
This results in two identical squares whose areas are 45 square units each.
To find the length of the side of the resulting square, we will use the formula for the area of a square.
A=s^2
Let's find the length of the side s by substituting 45 for A.
From Part A we know that the width of the rectangle is sqrt(45) units. We will estimate it to the nearest tenth by finding consecutive perfect squares around the number under the root. The two nearest perfect squares are 36 and 49.
We know that sqrt(45) is somewhere between 6 and 7. To approximate it to the nearest tenth we will use decimals between 6 and 7. Let's calculate the square of each number and compare them with 45.
Approximation
Square of Approximation
Comparison
6.1
6.1 * 6.1 = 37.21
Approximation is too low
6.2
6.2 * 6.2 = 38.44
Approximation is too low
6.3
6.3 * 6.3 = 39.69
Approximation is too low
6.4
6.4 * 6.4 = 40.96
Approximation is too low
6.5
6.5 * 6.5 = 42.25
Approximation is too low
6.6
6.6 * 6.6 = 43.56
Approximation is too low
6.7
6.7 * 6.7 = 44.89
Approximation is too low
6.8
6.8 * 6.8 = 46.24
Approximation is too high
We know that sqrt(45) is somewhere between 6.7 and 6.8. In order to estimate it to the nearest tenth, we need to find which square is closer. We will do this by finding the difference between 44.89 and 45, and 45 and 46.24.
45.89-0.11 ←45+1.24 →46.24
Because 45 is closer to 44.89, we know that sqrt(45) is closer to sqrt(44.89). Therefore, the nearest decimal number to sqrt(45) is 6.7. Since the length of the rectangle is twice its width, it will measure 2sqrt(45) units. We can estimate it to 13.4 units using the approximation of sqrt(45).
