SIMPLIFY RADICAL EXPRESSIONS WITH VARIABLES WORKSHEET

Simplify the expressions. Assume all variables represent positive rational number.

Solution

Problem 14 :

When 5 √20 is written in simplest radical form, the result is k√5. What is the value of k?

a)   20      b) 10      c) 7       d) 4

Solution

Problem 15 :

Which expression is equivalent to 7√90?

a) 16 √10     b) 21√10      c) 70 √9         d) 6√30

Solution

Problem 16 :

Multiply 4√3(2√3 - 3√6)

a) 16 √10     b) 21√10      c) 70 √9         d) 6√30

Solution

Problem 17 :

Multiply (3√x - √y)²

Solution

Problem 18 :

Marcy received a text message from Mark asking her how old she was. In response, Marcy texted back “125^(2/3) years old.” Help Mark determine how old Marcy is.

Solution

Problem 19 :

(1/2) √8 + (3/5) √50 - (2/3) √18

Solution

Expand and simplify :

Problem 1 :

(1 + √2) (2 + √2)

Solution

Problem 2 :

(2 + √3) (3 + √3)

Solution

Problem 3 :

(4 - √2) (3 + √2)

Solution

Problem 4 :

(1 + √3) (1 - √3)

Solution

Problem 5 :

(√5 + 2) (√5 - 3)

Solution

Problem 6 :

(6 - √3) (2 + √3)

Solution

Problem 7 :

(4 - 3√3) (2 - √3)

Solution

Problem 8 :

(-1 + 2√2) (2 - √2)

Solution

Problem 9 :

4√3 (2√3 - 3√6)

Solution

Problem 10 :

(3√x - √y)²

Solution

Problem 11 :

Area of the rectangle given below.

Solution

Problem 12 :

Area of the triangle given below.

Solution

Problem 13 :

Area of the triangle given below.

Solution

Problem 14 :

Area of the parallelogram given below.

Solution

Problem 15 :

Simplify 

-4 / (√3 - √5)

Solution

Problem 16 :

Simplify 

(√x + 2)/(3 - √x)

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

Problem 1 :

3√6 - 4√6

Solution

Problem 2 :

-3√7 + 4√7

Solution

Problem 3 :

-11√21 - 11√21

Solution

Problem 4 :

-9√15 + 10√15

Solution

Problem 5 :

-10√7 + 12√7

Solution

Problem 6 :

-3√17 - 4√17

Solution

Problem 7 :

-10√11 - 11√11

Solution

Problem 8 :

-2√3 + 3√27

Solution

Problem 9 :

2√6 - 2√24

Solution

Problem 10 :

2√6 + 3√54

Solution

Problem 11 :

-√12 + 3√3

Solution

Problem 12 :

3√3 - √27

Solution

Problem 13 :

3√8 + 3√2

Solution

Problem 14 :

-3√6 + 3√6

Solution

Find the perimeter of the shapes given below.

Problem 15 :

Solution

Problem 16 :

Solution

Problem 17 :

Solution

Problem 18 :

Solution

Problem 19 :

What are the perimeter and area of a rectangle with length of 5√3 cm and width of 3√2 cm ?

Solution

Problem 20 :

The sum of 2√8, 4√50 and 3√18 is

Solution

Problem 21 :

The difference between (1/2) √180 and (2/5) √20

Solution