PRACTICE QUESTIONS IN SIMPLIFYING RADICALS

Practice questions on simplifying radicals

Simplify the following radicals :

Solution

Practice questions on exponents and radicals

Simplify the following :

Practice questions on simplifying radicals with variables and exponents

Simplify the following radicals with variables :

Solution

Practice questions on operations with radicals

Simplify the following radical expression : 

1)  7√30 + 2√75 + 5√50                        Solution

2)  √27 + √105 + √108 + √45                  Solution

3)  √45 + 3√20 + √80 - 4√40                 Solution

4)  3√5 + 2√95 + 3√117 - √78               Solution

5)  3 √32 - 2√8 + √50                           Solution

6)  2 √12 - 3√27 - √243                       Solution

7)  √54 - √2500 - √24                          Solution

8)  √45 - √25 - √80                              Solution

9)  5√95 - 2√50 - 3√180                       Solution

10)  √5 x √18                                          Solution

11)  ∛7 x ∛8                                           Solution

12)  ∛13 x ∛5                                          Solution

13)  3√35 ÷ 2√7                                      Solution

14)  15√54 ÷ 3√6                                     Solution

15)  (48)^1/4 ÷ (72)^1/8                                     Solution

16)  4√3, 18√2, -3√3, 15√2                     Solution

17)  2∛2, 24∛2, - 4∛2                             Solution

Practice questions on rationalizing the denominator with surds

Rationalize the denominator :

Practice questions on rationalizing the denominator with variables

Rationalize the denominator :

1)  1/√x                                              Solution

2)  1/(x + √y)                                     Solution

3)  (√x + y) /  (x - √y)                        Solution

4)  (√x + √y)/√x                                Solution

5)  (√x + √y)/(√x - √y)                      Solution

6)  1/(x + y√3)                                  Solution

7)  ³√(2/3a)                                     Solution

8)  Simplify : √(12x²) / √(30x)         Solution

9)  √(100x/11y)                                 Solution

Answers :

1)  √x/x

2)  (x - √y) / (x² - y)

3)  [x√x + √xy + xy + y√y] / (x² - y²)

4)  [x + √(xy)]/x

5)  (x + 2√(xy) + y) / (x - y)

6)  (x - y√3) / (x² + 3y²)

7)  ³√(18a²) / 3a

8)  √10x / 5

9)  10√(11xy) / 11y

Practice questions on using distributive property with radicals

Expand and simplify the following radicals :

Solution

Practice questions on solving for unknown with radicals

Solve for unknown variables :

1)  (x + y√2) (2 - √2)  =  1+√2

2) (2 - 3√2)(x + y√2) = √2

3)  (x + y√2) (3 + √2)  =  1

4)  (a + √2) (2 - √2) =  4 - b√2

5)  (a + b√2)² =  33 + 20√2

6)  (x + y√2) (3 - √2)  = -4√2

Answers :

1)   x = 2 and y = 3/2

2)  x = -3/7 and y = -1/7

3)  x  =  3/7 and y = -1/7

4)  a = 3 and b = - 1

5)  a = 5 and b = 2

6)  x = -8/7 and y = -12/7

Solution

Problem 1 :

2√3(4 - √3)

Solution

Problem 2 :

- √2(2 - √2)

Solution

Problem 3 :

2√3(√3 - 1) - 2√3

Solution

Problem 4 :

(2√2 - 5)(1 - √2)

Solution

Problem 5 :

(3 + 2√5)(2 - √5)

Solution

Problem 6 :

(4 - √2)(3 + 2√2)

Solution

Problem 7 :

(3 - √7)²

Solution

Problem 8  :

- (2 - √5)²

Solution

Problem 9 :

(2 - √3)(2 + √3)

Solution

Problem 10 :

(5 - √3)(5 + √3)

Solution

Problem 11 :

Write √1/7 in the form k√7

Solution

Problem 12 :

Find x, y ∈ Q such that (3 + x√5) (√5 – y)  =  - 13 + 5√5

Solution

Problem 13  :

Find p, q  ∈ Q such that (p + 3√7) (5 + q√7)  =  9√7 - 53

Solution

Problem 14  :

Solve for m, √(m - 1) + 5 = m - 2

Solution

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