ADD AND SUBTRACT RADICAL EXPRESSIONS WORKSHEET

Simplify the following radical expressions :

Question 1 :

√3 + √12

Solution

Question 2 :

√75 + √3

Solution

Question 3 :

√18 + √98

Solution

Question 4 :

√5 + √20 - √125

Solution

Question 5 :

√5 + 3√7 - 4√5 - 5√7

Solution

Question 6 :

3√3 + 4√3 - √2

Solution

Question 7 :

2(√5 - √3) + 3(√3 - √5)

Solution

Question 8 :

³√16 + ³√54

Solution

Question 9 :

√25 + 5³√64

Solution

Question 10 :

8³√686 - 5³√250

Solution

Question 11 :

√(12w) + √(27w)

Solution

Question 12 :

 √45y³ + √25y³

Solution

Question 13 :

³√8x³y⁶ + √9x²y⁴

Solution

Question 14 :

√4p²q⁴ - ³√125p³q⁶

Solution

Question 15 :

A square has sides each measuring 2√7 feet. Determine the area of the square.

Solution

Question 16 :

The period of a pendulum is the time required for it to make one complete swing back and forth. The formula of the period P of the pendulum is P = 2 π√(l/32), where l is the length of the pendulum in feet. If a pendulum in a clock tower is 8 feet long, find the period. Use 3.14 for  π.

Solution

Question 17 :

A rectangle has width 3√5 centimeters and length 4√10 centimeters. Find the area of the rectangle.

Solution

Question 18 :

A rectangle has length √(a/8) meters and width √(a/2) meters. What is the area of the rectangle ?

Solution

Question 19 :

The formula for the area A of the square with side length s is A = s². Solve this equation for s, find the side length of a square having an area of 72 square units.

Solution

Question 20 :

Find the area of the rectangle 

Problem 1 :

The formula for the kinetic energy of a moving object is

E = (1/2) mv²

where E is the kinetic energy in joules, m is the mass in kilograms and v is the velocity in meters per second.

a) solve the equation for v.

b) Find the velocity of an object whose mass is 0.6 kilograms and whose kinetic energy is 54 joules.

Solution

Problem 2 :

Police officers can use the formula s = √(30 fd) to determine the speed s that a car was travelling in miles per hour by measuring the distance d is feet of its skid marks. In this formula f is the coefficient of friction for the type and condition of the road.

a)  Write a simplified expression for the speed if f = 0.6 for a wet asphalt road.

b)  What is the simplified expression for the speed if f = 0.8 for a dry asphalt road ?

c) an officer measures skid marks that are 110 feet long. Determine the speed of the car for both wet road conditions and for dry road conditions.

Solution

Problem 3 :

If the cube has a surface area of 96 a², what is the volume ?

a)  32 a³     b)  48 a³    c)  64 a³     d) 96 a³

Solution

Problem 4 :

If x = 81 b² and b > 0, then  √x = ?

a)  -9b     b)  9b    c)  3b√27     d) 27b√3

Solution

Problem 5 :

Find the perimeter and the area of a square whose sides measure 4 + 3√6 feet.

Solution

Problem 6 :

The voltage V required for a circuit is given by V = √PR, where P is the power in watts and R is the resistance in ohms. How many more volts are needed to light a 100 watt bulb that a 75 watt bulb if the resistance for both is 110 ohms ?

Solution

Problem 7 :

Find the perimeter of a rectangle whose length is 8√7 + 4√5 inches and whose width is 5√7 - 3√5 inches

Solution

Problem 8 :

The perimeter of the rectangle is 2√3 + 4√11 + 6 centimeters and its length is 2√11 + 1 centimeters. Find the width.

Solution

Problem 9 :

Two objects are dropped simultaneously. The first object reaches the ground in 2.5 seconds, and the second object reaches the ground 1.5 seconds later. From what heights were the two objects dropped ?

t = √h / 4

Solution

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