Solve 1.331<1.05n^2

$$1.331 < 1.05 n ^ { 2 }$$

Solve for n

$$n\in \left(-\infty,-\frac{11\sqrt{462}}{210}\right)\cup \left(\frac{11\sqrt{462}}{210},\infty\right)$$

Solution Steps

Divide both sides by 1.05. Since 1.05 is positive, the inequality direction remains the same.

$$\frac{1.331}{1.05}<n^{2}$$

Expand \frac{1.331}{1.05} by multiplying both numerator and the denominator by 1000.

$$\frac{1331}{1050}<n^{2}$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$n^{2}>\frac{1331}{1050}$$

Calculate the square root of \frac{1331}{1050} and get \frac{11\sqrt{462}}{210}. Rewrite \frac{1331}{1050} as \left(\frac{11\sqrt{462}}{210}\right)^{2}.

$$n^{2}>\left(\frac{11\sqrt{462}}{210}\right)^{2}$$

Inequality holds for |n|>\frac{11\sqrt{462}}{210}.

$$|n|>\frac{11\sqrt{462}}{210}$$

Rewrite |n|>\frac{11\sqrt{462}}{210} as n<-\frac{11\sqrt{462}}{210}\text{; }n>\frac{11\sqrt{462}}{210}.

$$n<-\frac{11\sqrt{462}}{210}\text{; }n>\frac{11\sqrt{462}}{210}$$