SIMPLIFYING RADICAL EXPRESSIONS WORKSHEET

Simplify the radical expression using the definition.

Problem 1 :

√(4(y - 1)²)             Solution

Problem 2 :

∛(-8x³y⁶)          Solution

Problem 3 :

5^th root (2x - 1)⁵          Solution

Problem 4 :

 ∜(16x⁸)          Solution

Problem 5 :

∛(-27x³)          Solution

Problem 6 :

 ∜(16a¹²y²)          Solution

Problem 7 :

√x / ∛x          Solution

Problem 8 :

√(∛x)          Solution

Problem 9 :

√(x+7)√(x-7)          Solution

Problem 10 :

√50          Solution

Problem 11 :

Add or subtract the following radicals. Write answers in simplified form. 

Solution

Example 12 :

Rationalize the denominators and simplify (assume all variables represent positive real numbers).

Solution

Simplify radical expressions

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

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

Practice on adding and subtracting radicals.

Problem 1 :

5√6 + 3√6

Solution

Problem 2 :

4√20 - 2√5

Solution

Problem 3 :

3√(32x²) + 5x√8

Solution

Problem 4 :

7√4x² + 2√25x - √16x

Solution

Problem 5 :

5∛x²y + ∛27x⁵y⁴ 

Solution

Problem 6 :

3√9y³ - 3y√16y + √25y³

Solution

Problem 7 :

√(248 + (√(51 + √169))

Solution

Problem 8 :

If a * b * c = √(a + 2) (b + 3) / (c + 1) then find the value of 6 * 15 * 3

Solution

Problem 9 :

What will come in the place of question mark in each of the following :

i)  √(32.4/?) = 2

ii)  √86.49 + √(5 + ?²) = 12

Solution

Problem 10 :

If √1 + (x/144) = 13/12, find the value of x

Solution

Problem 11 :

If x = 1 + √2 and y = 1 - √2, find the value of x² + y²

Solution

Problem 12 :

√(10 + (√25 + (√108 + (√154 + (√225))))) is 

Solution

Problem 1:

√36

Solution

Problem 2 :

√4

Solution

Problem 3 :

√64

Solution

Problem 4 :

√144

Solution

Problem 6 :

-√100

Solution

Problem 7 :

-√1

Solution

Problem 8 :

-√121

Solution

Problem 9 :

√-36

Solution

Problem 10 :

√-9

Solution

Problem 11 :

√-49

Solution

Problem 12:

√(9 + 16)

Solution

Problem 13:

√25 + 144

Solution

Problem 14 :

√9 + √16

Solution

Problem 15 :

√25 + √144

Solution

Problem 16 :

Find the square root of 6400

Solution

Problem 17 :

Is 2352 a perfect square? If not find the smallest multiple of 2352 which is a perfect square. Find the sqaure root of the new number.

Solution

Problem 18 :

2116 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

Solution

Problem 19 :

A natural number is called a _________ or _____________ if it is the square of some natural numbers 

Solution

Problem 20 :

Simplify √0.09

Solution

Problem 21 :

Find the length of the side of a square whose area is 441 m²

Solution