Question

10

Which inequalities are true? Select the four correct answers.
O V5 <2.3 0 V5 <24 < V6
O Vac5c √5.5
OVE <3 <3
O V <2.9 <
O4 <4.5<5

Answer 1

A, B, C, E

Explanation:

Here, you're being asked to put sets of three numbers in order. In many cases, two of the three numbers are irrational square roots. It can work well here to recognize that the order doesn't change if the numbers are squared. By squaring the numbers involved we can make an easier comparison of rational numbers.

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a) √5 < 2.3 < √6 ⇒ 5 < (2.3² = 5.29) < 6 . . . . true

b) √5 < 2.4 < √6 ⇒ 5 < (2.4² = 5.76) < 6 . . . . true

c) √4 < √5 √5.5 ⇒ 4 < 5 < 5.5 . . . . true

d) √8 < 3 < √9 ⇒ 8 < (3² = 9) < 9 . . . . false

e) √8 < 2.9 < 9 ⇒ 8 < (2.9² = 8.41) < 9 . . . . true

f) √4 < 4.5 < √5 ⇒ 4 < (4.5² = 20.25) < 5 . . . . false