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

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

Answer 2

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

Explanation:

Consider the diagram below for the number line.

• The first statement is:
  `√(2)<2`

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

• The second statement is:
  `√(2)<√(3)`

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

• The third statement is:
  `√(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:
  `√(3)<3`

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

• The fifth statement is:
  `√(2)=√(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:
  `√(3)=√(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.