SIMPLIFYING RADICALS

Problem 1 :

What is √32 expressed in simplest radical form ?

1)  16√2        2)  4√2      3)  4√8       4)  2√8

Solution :

√32 = √(16 × 2)

 = √(4 × 4 × 2)

= 4√2

Hence, √32 expressed in simplest radical form is 4√2.

So, option 2) is correct.

Problem 2 :

The expression √50 can be simplified to

1)  5√2       2)  5√10       3)  2√25      4)  25√2

Solution :

√50 = √(25 × 2)

 = √(5 × 5 × 2)

= 5√2

So, option 1) is correct.

Problem 3 :

What is √72 expressed in simplest radical form ?

1)  2√18      2)  3√8         3)  6√2       4)  8√3

Solution :

√72 = √(36 × 2)

 = √(6 × 6 × 2)

= 6√2

Hence, √72 expressed in simplest radical form is 6√2.

So, option 3) is correct.

Problem 4 :

When √72 is expressed in simplest a√b form, what is the value of a ?

1)  6       2)  2       3)  3          4)  8

Solution :

√72 = √(36 × 2)

 = √(6 × 6 × 2)

= 6√2

So, a is 6 and b is √2 . Then, the value of a is 6.

So, option 1) is correct.

Problem 5 :

The expression √150 is equivalent to

1)  25√6      2)  15√10      3)  5√6       4)  6√5

Solution :

√150 = √(25 × 6)

 = √(5 × 5 × 6)

= 5√6

Hence, the expression √150 is equivalent to 5√6.

So, option 3) is correct.

Problem 6 :

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

1)  20      2)  10         3)  7        4)  4

Solution :

5√20 = 5√(5 × 4)

 = 5 × 2 × √5

= 10√2

Hence, the value of k is 10.

So, option 2) is correct.

Problem 7 :

What is 2√45 expressed in simplest radical form ?

1)  3√5       2)  5√5      3)  6√5     4)  18√5

Solution :

2√45 = 2√(9 × 5)

 = 2√(3 × 3 × 5)

= 2 × 3√5

= 6√5

Hence, 2√45 expressed in simplest radical form is 6√5.

So, option 3) is correct.

Problem 8 :

Which expression is equivalent to 7√90 ?

1)  16√10   2)  21√10     3)  70√10      4)  √630

Solution :

7√90 = 7√(10 × 9)

 = 7√(3 × 3 × 10)

= 7 × 3√10

= 21√10

Hence, the expression 21√10 is equivalent to 7√90

So, option 2) is correct.

Problem 9 :

What is 3√250 expressed in simplest radical form ?

1)  5√10    2)  8√10     3)  15√10    4)  75√10

Solution :

3√250 = 3√(25 × 10)

 = 3 × √(5 × 5 × 10)

= 3 × 5√10

= 15√10

Hence, 3√250 expressed in simplest radical form is 15√10.

So, option 3) is correct.

Problem 10 :

What is √32/4 expressed in simplest radical form ?

1)  √2     2)  4√2      3)  √8       4)  8√2

Solution :

√32/4 = √(16 × 2)/4

= (√(4 × 4 × 2)/4

= (4 × √2)/4

= √2

Hence ,√32/4 expressed in simplest radical form is √2.

So, option 1) is correct.

Problem 11 :

Simplify : √12

Solution :

 √12 = √(4 × 3)

 = √(2 × 2 × 3)

= 2√3

Problem 12 :

Simplify : √75

Solution :

√75 = √(25 × 3)

 = √(5 × 5 × 3)

= 5√3

Problem 13 :

Simplify : √128

Solution :

√128 = √(64 × 2)

 = √(8 × 8 × 2)

= 8√2

Problem 14 :

Simplify : 3√27

Solution :

3√27 = 3√(9 × 3)

 = 3√(3 × 3 × 3)

= 3 × 3√3

= 9√3

Problem 15 :

Express -3√48 in simplest radical form.

Solution :

-3√48 = -3√(16 × 3)

 = -3√(4 × 4 × 3)

= -3 × 4√3

= -12√3

Problem 16 :

Express 5√72 in simplest radical form.

Solution :

5√72 = 5√(36 × 2)

 = 5√(6 × 6 × 2)

= 5 × 6√2

= 30√2

Problem 17 :

Express 4√75 in simplest radical form.

Solution :

4√75 = 4√(25 × 3)

 = 4√(5 × 5 × 3)

= 4 × 5√3

= 20√3

Problem 18 :

Express 2√108 in simplest radical form.

Solution :

2√108 = 2√(36 × 3)

 = 2√(6 × 6 × 3)

= 2 × 6√3

= 12√3

Problem 19 :

Theo determined that the correct length of the hypotenuse of the right triangle in the accompanying diagram is √20. Fiona found the length of the hypotenuse to be 2√5. Is Fiona ‘ s answer also correct ? justify your answer.

Solution :

(AC)² = (AB)² + (BC)²

x² = (2)² + (4)²

x² = 4 + 16

x² = 20

x = √20

x = √(4 × 5)

x = 2√5

Yes she is correct.