Square Root Functions
What is the domain and range of the following Square Root Function?
Square Root Function: f(x) = √(x + 2)
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
What is 'x ≥ -2 and y ≥ 0'?
Simplify the Radical Expression: 2√196
What is '28'?
8√7 + 54√7 - 48√7
What is '14√7'?
Solve for x: √(x + 9) - 21 = 6
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
What is 'x = 720'?
Determine whether the numbers: 20, 21, 29 can be lengths of a right-angled triangle.
Yes, the numbers: 20, 21, and 29 can be lengths of a right-angled triangle.
What is the domain and range of the following Square Root Function?
f(x) = -3√(x +2) + 5
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
What is 'x ≥ -2 and y ≤ 5'?
Rationalize the Radical Expression: (24√3)/√5
What is '(24√15)/5'?
2(7√3 + 3√81 + 12√27)
What is '86√3 + 54'?
Solve for k: √(2k + 3 + k) + 5 = 10
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
What is 'k = 22/3'?
The hypotenuse of a right-angled triangle is 10 feet. The length of one leg is 6 feet. Using the Pythagorean Theorem, find the length of the other leg. Round to the nearest hundredth if necessary.
The length of the second leg is 8 feet.
Compare f(x) = -2√(x + 2) to the parent function
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
The parent function will have to be reflected across the x-axis, stretched vertically, and translated 2 units to the left to become the new function.
Rationalize the Radical Expression: (√5)/(5 - 2√5)
What is '√5 + 2'?
(3√5 + 2√8)(5√2 + 7√5)
What is '43√10 + 145'?
Solve for x: √(3x/2) - 3 = 9
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
What is 'x = 96'?
The area of a square is 1600 centimeters. Find the distance between opposite corners using the Pythagorean Theorem. Round to the nearest hundredth if necessary.
The distance between the opposite corners of the square is around 56.57 cm.
Compare f(x) = 0.8√(x - 9) + 3 to the parent function. Afterwards, state the domain and range.
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
The parent function will have been compressed vertically and translated 9 units to the right and 3 units up to become the new function. The domain of this function is x ≥ 9 and the range is y ≥ 3.
Rationalize the Radical Expression: (√54a5b6)/(√24b4)
What is '(3a2b√a)/2'?
(√3)/√7 + √21
What is '(8√21)/7'?
Solve for x: √(3x + 27) = x + 3
Important: ONLY the NUMBERS inside the PARENTHESIS are PART of the square root
What is 'x = 3'?
Sid constructs a ladder measuring 13 feet. She leans it against a wall measuring 12 feet. How far away is the ladder from the wall? Round to the nearest hundredth if necessary.
The ladder is 5 feet away from the wall.
Challenge Problem: Identify the equation that doesn't belong. Explain.
1. 0.2√(x)
2. 2√x
3. (√x)/3
The second equation doesn't belong. Unlike the other two functions, the 2nd function is stretched vertically. The 1st and 3rd functions are compressed vertically.
Challenge Problem: (2√2 + 3)/(1 - √2)
What is '-5√2 - 7'?
Challenge Problem: The area of a trapezoid is represented by this formula: area = 1/2(a + b)(h). The variable, a represents the bottom base of the trapezoid. The variable, b represents the top base of the trapezoid. The variable, h represents the height. If a = √324, b = 2 + √4, h = (√81)/√5, find the area of the trapezoid.
What is '(99√5)/5'?
Challenge Problem: The perimeter of a rectangle is represented by this expression: 8x + 22√x - 6. The length is twice the width. The width is given as x + 3√x. What is the value of x?
What is 'x = 1'?
Challenge Problem: Find the values of a, b, c:
a = 1/5(x) - 12
b = x - 1
c = x
What is 'a = 17, b = 144, and c = 145'?