Mathematics 10 Quiz Bowl

EASY (1min)

1

Which of the following pairs of radical expressions represents similar radicals?

A) √5 and 3√5

B) √2 and 2√3

C) √7 and ³√7

D) 3√x and 3√y

A) √5 and 3√5

1

What is the simplified sum of √5 + 3√5?

A) 4√10

B) 4√5

C) 3√5

D) 3√25

B) 4√5

1

Perform the indicated operation: 2√3 - 7√3.

A) 5√3

B) -5√3

C) -9√3

D) -5√6

B) -5√3

1

. What is the essential first step when adding or subtracting radicals that are not initially like radicals?

A) Add all radicands together directly.

B) Multiply the coefficients by the index.

C) Simplify each radical expression completely.

D) Square both radical expressions.

C) Simplify each radical expression completely.

1

10. Rationalize the denominator of the fraction: 5 / √2.

A) (5√2) / 2

B) √10 / 2

C) 5√2

D) 25 / 2

D. Core Outcome

A) (5√2) / 2

MODERATE (2mins)

1

Simplify completely: √8 + 3√18 - √2.

A) 11√2

B) 10√2

C) 3√24

D) 4√2

B) 10√2

1

Perform the indicated operation: 6³√2 - ³√16.

A) 4³√2

B) 5³√2

C) 4³√14

D) 2³√2

A) 4³√2

1

Combine like terms: 3√5 + √3 - 2√3 + √5.

A) 4√5 - √3

B) 2√5 + 3√3

C) 4√2

D) 3√8

 A) 4√5 - √3

1

Find the product of 5√3x · 7√5y.

A) 35√15xy

B) 12√8xy

C) 35√8xy

D) 15√35xy

A) 35√15xy

1

Simplify the quotient: √(32x³) / √(2x).

A) 16x²

B) 4

C) 4x√2

D) 2x

B) 4

DIFFICULT (3mins)

1

Multiply radicals having different orders and different radicands: √2 · ³√5.

A) ⁶√200

B) ⁶√10

C) ⁵√10

D) ⁶√100

D) ⁶√100

1

Rationalize the binomial denominator: 2x / (5 + √2).

A) (10x - 2x√2) / 23

B) (10x + 2x√2) / 23

C) (10x - 2x√2) / 27

D) 2x(5 + √2) / 23

A) (10x - 2x√2) / 23

1

Multiply and simplify completely: √(18xy³) · √(50x³).

A) 30x²y√y

B) 30x²y²√y

C) 15x²y√2y

D) 900x⁴y³

A) 30x²y√y

1

Simplify the expression involving variable cube roots: 6³√(2x³) - 2x³√2.

A) 4x³√2

B) 4³√(2x³)

C) 8x³√2

D) 4x³√x

A) 4x³√2

1

Find the product: √(2m) ³√(2m).

A) ⁶√(32m⁵)

B) ⁶√(4m²)

C) ⁵√(4m²)

D) 2m⁶√(2m)

Work Immersion

BONUS QUESTION

1

Find the product: 2√10 · 3√2.

A) 6√20

B) 12√5

C) 6√5

D) 12√10

B) 12√5

1

Multiply radicals with different orders but the same radicand: √3 · ³√3.

A) ⁶√243

B) ⁶√9

C) ⁵√9

D) 3⁶√3

A) ⁶√243

1

Multiply the monomial radical by the binomial: √3(√8 + 2√3).

A) 2√6 + 6

B) √24 + 6√3

C) 6√2 + 2

D) 2√24 + 6

A) 2√6 + 6

1

Find the product of the conjugate binomials: (√3 + √5)(√3 - √5).

A) -2

B) 8

C) 3 - 2√15

D) -8

A) -2

1

Divide and rationalize the denominator: ³√2 / ³√5.

A) ³√50 / 5

B) ³√10 / 5

C) ³√25 / 5

D) 2 / 5

A) ³√50 / 5