MULTIPLYING BINOMIAL RADICAL EXPRESSIONS WORKSHEET

Expand and simplify :

Problem 1 :

(1 + √2) (2 + √2)

Solution

Problem 2 :

(2 + √3) (3 + √3)

Solution

Problem 3 :

(√3 + 2) (√3 – 1)

Solution

Problem 4 :

(4 - √2) (3 + √2)

Solution

Problem 5 :

(1 + √3) (1 - √3)

Solution

Problem 6 :

(5 + √7) (2 - √7)

Solution

Problem 7 :

(√5 + 2) (√5 – 3)

Solution

Problem 8 :

(6 - √3) (2 + √3)

Solution

Problem 9 :

(4 - √2) (3 - √2)

Solution

Problem 9 :

(4 - √2) (3 - √2)

Solution

Problem 11 :

(-1 + 2√2) (2 - √2)

Solution

Problem 12 :

(2√2 + 3) (2√2 + 5)

Solution

Problem 13 :

The ratio of the length to the width of a golden rectangle is (1 + √5) : 2. The dimensions of the face of the Parthenon in Greece form a golden rectangle. What is the height h of the Parthenon?

Solution

Problem 14 :

A rectangular walkway is √5 ft wide and 8√5 ft long. Find the perimeter of the walkway.

Solution

Problem 15 :

The process of eliminating a radical from the denominator of a radical expression is called _______________.

Solution

Problem 1 :

√6 × 4√6

Solution

Problem 2 :

-√5 × √20

Solution

Problem 3 :

-√2 × √3

Solution

Problem 4:

4√8 × √2

Solution

Problem 5 :

√12×√15

Solution

Problem 6 :

√5 × (-2√5)

Solution

Problem 7 :

-3√5 ×√20

Solution

Problem 8 :

√15 × 3√5

Solution

Problem 9 :

√9 ×√3

Solution

Problem 10 :

-4√8 ×√10

Solution

Problem 11 :

Express (√3 - √2)² in simplest form.

Solution

Problem 12 :

The radius of the circle is 3√5 cm. If a square is inscribed in a circle 

a) determine the exact length of the diagonal of a square

b)  Determine the exact perimeter of the square.

Solution

Problem 13 :

The length of a rectangle is 2 √48 and width is 6√3. Express in the simplest form.

a) The area of the rectangle

b) The perimeter of the rectangle.

Solution

Problem 14 :

The area of the rectangle is 20√50 and length is 4√2, what is the width ?

Solution

Problem 15 :

If the perimeter of the rectangle is 12√3 and the length is 2√12, what is the width ?

Solution

Problem 16 :

The area of the parallelogram is 8√90 and the base is 2√5. What is the height of the parallelogram ?

Solution

Expand and simplify :

Problem 1 :

(4 + √3) (4 - √3)

Solution

Problem 2 :

(5 - √2) (5 + √2)

Solution

Problem 3 :

(√5 - 2 ) (√5 + 2)

Solution

Problem 4 :

(√7 + 4 ) (√7 - 4)

Solution

Problem 5 :

(3√2 + 2 ) (3√2 - 2)

Solution

Problem 6 :

(2√5 - 1 ) (2√5 + 1)

Solution

Problem 7 :

(5 - 3√3) (5 + 3√3)

Solution

Problem 8 :

(2 - 4√2) (2 + 4√2)

Solution

Problem 9 :

(1 + 5√7) (1 - 5√7)

Solution

Problem 10 :

Find the area of the rectangle shown in the figure

Solution

Problem 11 :

Find the area of the rectangle shown in the figure

Solution

Problem 12 :

Complete the statement √2 √5 = √10 because

Solution

Problem 13 :

Complete the statement 2√3 + 5√3 = 7√3 but 7√3 + 3√5 ≠ 10√8

Solution

Problem 14 :

The radius r of a sphere is given by

r = ³ √(3/4π) V

where V is the volume of the sphere. Estimate the volume of a spherical head of brain coral with a radius of 1.5 feet.

Solution

Problem 15 :

The mean sustained wind velocity (in meters per second) of a hurricane is modeled by

v( p) = 6.3 √(1013 − p)

where p is the air pressure (in millibars) at the center of the hurricane. Estimate the air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second.

Solution

Problem 16 :

The maximum speed v (in meters per second) of a trapeze artist is represented by

v = √2gh

where g is the acceleration due to gravity (g ≈ 9.8 m/sec²) and h is the height (in meters) of the swing path. Find the height of the swing path for a performer whose maximum speed is 7 meters per second.

Solution

Answer Key

1) 13

2) 23

3) 1

4) -9

5) 14

6) 19

7) -2

8) -28

9)  -174

10) √33 square units.

11) 8 + 2√15

12) √a x √b = √(a x b)

13) they are not like terms, so we cannot add them

14) V = 14.13

15) p = 938.17

16) h = 2.5