Inequalities with Powers, Roots, and Radicals
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- So far, we've seen pretty simple inequalities with linear and polynomial terms. But those are not the only types of inequalities we can have! Just like equations, inequalities c…
By Anusha Rahman
- (Video) Solve an Inequality with a Square Root by Brian McLogan In this video by Brian McLogan, you will be able to walk through an example of solving an inequality with a squar…
By Anusha Rahman
- Inequalities with Powers, Roots, and Radicals We know that inequalities compare two values using symbols like >>>, <<<, ≥\geq≥, and ≤\leq≤. When we add powers or roots to inequa…
By Anusha Rahman
Problems 5
- What is the smallest positive number satisfying the inequality x≤2x\sqrt x \leq 2xx≤2x?
- Which of these numbers satisfy 3x>xx3 \sqrt{x} > x \sqrt{x}3x>xx?
- Which of the following is the set of all solutions to 4x≥x+34 \sqrt{x} \ge x + 34x≥x+3?
- Which of the following integers satisfy (6−42)x+22>x\sqrt{(6 - 4\sqrt{2})x} + 2 \sqrt{2} > x(6−42)x+22>x?
- How many integers satisfy sin(xπ2)cos(xπ2)+1>x\sqrt{\sin(\frac{x\pi}{2}) \cos(\frac{x\pi}{2})} + 1 > xsin(2xπ)cos(2xπ)+1>x?