SIMPLEST RADICAL FORM

Problem 1 :

What is √45 in simplest form?

a. 5√3     b. 9√5     c. 3√5     d. 15√3

Solution :

√45 = √(9 × 5)

= √9 × √5

= 3√5

So, option (c) is correct.

Problem 2 :

What is √90x⁵ y⁴ in simplest radical form?

a. 10x²y² √9x       b. 9x³y² √10x²y²

c. 3x²y² √10x        d. 18x⁴y³ √5xy

Solution :

√90x⁵ y⁴ = √ (9 × 10xx⁴y⁴)

= √ (3² x⁴y⁴ 10x)

= √3² √x⁴ √y⁴ √10x

= 3x²y² √10x

So, option (c) is correct.

Problem 3 :

Which radical expression when expressed in simplified form is 3√13?

a. √16     b. √39      c. √117      d. √507

Solution :

3√13 = 3 × √13

= √39

So, option (b) is correct.

Problem 4 :

Which value could replace the? to make the expression true?

√12a⁶b³ = 2a³b√?

a. 6b²       b. 3b      c. 4a³b²     d. 3a²b

Solution :

= √12a⁶b³

= √(4 ∙ 3a⁶b²b)

= √(2² ∙ b²a⁶ ∙ 3b)

= √2² ∙ √b² ∙ √a⁶ ∙ √3b

= 2a³b ∙ √3b

So, option (b) is correct.

Problem 5 :

For what value of x does ∛x simplify to 4∛5?

a. 20     b. 80      c. 320     d. 460

Solution :

∛x = 4∛5

x = (4∛5)³

x = 4³ (∛5)³

x = 64 × 5

x = 320

So, option (c) is correct.

Problem 6 :

If y³ = -56, what is the value of y?

a. -2∛14    b. -8∛7     c. -2∛7     d. -7∛8

Solution :

y³ = -56

y = ∛ (-56)

y = -∛ (8 × 7)

y = - ∛8 ∛7

y = -2∛7

So, option (c) is correct.

Problem 7 :

Write the radical expression ∛-216 in simplest form.

Solution :

= ∛-216

= ∛-6 ∙ -6 ∙ -6

= -6

Problem 8 :

Which value could replace the? To make expression true?

∛486 = 3∛?

Solution :

∛486 = 3∛x

= ∛ (3³ ∙ 18)

= ∛ (3³) ∙ ∛18

= 3∛18

Problem 9 :

∛24 - 7√3

Solution :

= ∛24 - 7√3

= ∛ (2³ ∙ 3) - 7√3

= ∛ 2³ ∙ ∛3 - 7√3

= 2∛3 - 7√3

Problem 10 :

8√2 + 3√8

Solution :

= 8√2 + 3√8

= 8√2 + 3 √ (2² ∙ 2)

= 8√2 + 3 (√2² ∙ √2)

= 8√2 + 3(2 ∙ √2)

= 8√2 + 6√2

= 14√2

Problem 11 :

(-5√36) (3√2)

Solution :

= (-5√36) (3√2)

= (-5 × 6) (3√2)

= -30 × 3√2

= -90√2

Problem 12 :

(3a²√3) (a√12)

a. 3a³√15    b. 18a³    c. 4a⁴√12    d. 9a³√2

Solution :

= (3a²√3) (a√12)

= (3a²√3) (a√ (4 ∙ 3))

= (3a²√3) (2a√3)

= 6a³ (√3 ∙ √3)

= 6a³ (3)

= 18a³

So, option (b) is correct.