Exercise 7 Page 22

We want to compare and order 5.2, - 5.6, 3 910, and sqrt(21). To do so, we will approximate the value of these numbers and plot them on a number line. Notice that 5.2 is already in decimal form. We will start by expanding - 5.6. - 5.6 = - 5.6666... Now we can round it to the nearest tenth. - 5.6 ≈ - 5.7Notice that - 5.6 is the only negative number, so we can be sure that it will be the smallest of the given numbers since all of the other numbers are positive. The next step is to write 3 910 as a decimal. 3 910 = 3.9 Finally, we will approximate sqrt(21) by using perfect squares. The two nearest perfect squares are 16 and 25.

sqrt(16) < sqrt(21) < sqrt(25)

CalcRoot

Calculate root

4 < sqrt(21) < 5

Let's find the better approximation by using decimals. To do this, we will choose several decimals between 4 and 5. Then, we will calculate the square of each number and compare them with 21.

Approximation	Square of Approximation	Comparison
4.1	4.1 * 4.1 = 16.81	Approximation is too low
4.2	4.2 * 4.2 = 17.64	Approximation is too low
4.3	4.3 * 4.3 = 18.49	Approximation is too low
4.4	4.4 * 4.4 = 19.36	Approximation is too low
4.5	4.5 * 4.5 = 20.25	Approximation is too low
4.6	4.6 * 4.6 = 21.16	Approximation is too high

We know that sqrt(21) is between 4.5 and 4.6. Let's now mark all the approximations on a number line.

We can conclude that - 5.6 < 3 910 < sqrt(21) < 5.2.