Radical Equations Worksheets Grade 9

1. Mere is a park designer creating a new walking trail. The trail includes a suspension bridge over a small ravine. The height h (in meters) of the main cable above the bridge deck at a horizontal distance x (in meters) from the left tower is modeled by the function h(x) = sqrt(4x + 21). For safety reasons, a support beam must be placed exactly where the cable is 9 meters above the deck. What horizontal distance x from the left tower should Mere place the support beam?
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is inscribed inside this triangle such that it touches all three sides. What is the radius of this inscribed circle?
3. √(2x + 3) = 5

…and 4 more problems

1. A marine biologist is studying the relationship between water depth and light intensity in a coral reef. The light intensity I (in lumens) at depth d (in meters) is given by the formula I = 120/√(d + 4). If the light intensity measures 24 lumens at a certain depth, what is the depth in meters?
2. Charlotte is a physicist studying the motion of a pendulum. The time T (in seconds) for one complete swing is modeled by the equation T = 2π√(L/9.8), where L is the length of the pendulum in meters. In a specific experiment, she measures the time for one swing as 2π seconds. What is the length of the pendulum in meters?
3. Emma is a materials scientist testing a new alloy. The length L (in centimeters) of a metal rod under tension follows the equation L = sqrt(5x + 75), where x is the force applied in Newtons. If the rod's length is measured as 15 centimeters, what force x (in Newtons) is being applied?

…and 4 more problems

1. The sum of a number and its square root is 12. Find the number.
2. Charlotte is designing a suspension bridge for a science fair project. The parabolic main cable of her bridge is modeled by the equation y = sqrt(2x + 27), where y is the height of the cable in centimeters above the bridge deck at a horizontal distance x centimeters from the left tower. Charlotte wants to place a vertical support beam at the point where the cable is exactly 7 centimeters above the deck. At what horizontal distance x from the left tower should she place the support beam?
3. √(3x + 7) = 4

…and 4 more problems