3<x^2<5

The solution to 3<x^2<5 is -sqrt(5)<x<-sqrt(3)\lor sqrt(3)<x<sqrt(5)

Solution

3 < x^{2} < 5

- 5 < x < - 3 or 3 < x < 5

Interval Notation

(- 5, - 3) \cup (3, 5)

Decimal Notation

- 2.23606 \dots < x < - 1.73205 \dots or 1.73205 \dots < x < 2.23606 \dots

Solution steps

3 < x^{2} < 5

a < u < b

then

a < u and u < b

3 < x^{2} and x^{2} < 5

3 < x^{2} : x < - 3 or x > 3

x^{2} < 5 : - 5 < x < 5

Combine the intervals

(x < - 3 or x > 3) and - 5 < x < 5

Merge Overlapping Intervals

- 5 < x < - 3 or 3 < x < 5

- 2 < 4 x - 10 < 6

x < 220 < x + 1

0 < x < 30

- 4 \leq x^{2} \leq - 1

x - 7 < x - 1 < 8

What is 3<x^2<5 ?
The solution to 3<x^2<5 is -sqrt(5)<x<-sqrt(3)\lor sqrt(3)<x<sqrt(5)