Question

Plot √2 and √3 on the number line.

Which statements are true? Check all that apply.
StartRoot 2 EndRoot < 2
StartRoot 2 EndRoot < StartRoot 3 EndRoot
StartRoot 2 EndRoot > 1.5
StartRoot 3 EndRoot < 3
StartRoot 2 EndRoot is about 0.5 less than StartRoot 3 EndRoot.
StartRoot 3 EndRoot is about 0.3 greater than StartRoot 2 EndRoot.

Answer 1

Answer:

The statements (1), (2), (4) and (6) are true.

Step-by-step explanation:

Consider the diagram below for the number line.

• The first statement is: $\sqrt{2}<2$

From the number line it is clear that the above statement is true.

• The second statement is: $\sqrt{2}<\sqrt{3}$

From the number line it is clear that the above statement is true.

• The third statement is: $\sqrt{2}>1.5$

The value of √2 is 1.414. This value is less than 1.5.

So, the above statement is false.

• The fourth statement is: $\sqrt{3}<3$

From the number line it is clear that the above statement is true.

• The fifth statement is: $\sqrt{2}=\sqrt{3}-0.5$

The value of √3 is 1.732. The difference between √2 and √3 is, 0.318.

Thus, the above statement is false.

• The sixth statement is: $\sqrt{3}=\sqrt{2}+0.3$

The value of √3 is 1.732. The difference between √2 and √3 is, 0.318.

Implying, √3 = √2 + 0.318.

⇒√3 = √2 + 0.3

Thus, the above statement is true.

Answer 2

1,2,4,6 are the correct options.