Worksheet: Rationalizing Denominators of Radicals

In this worksheet, we will practice rationalizing denominators of radicals.

Q1:

Given that 𝑥=572 and 𝑦=72, find 𝑥+𝑦 expressing your answer in simplest form.

  • A28
  • B56
  • C 2 7
  • D8
  • E 2 2

Q2:

Simplify 12523135 by rationalizing the denominator.

  • A 1 1 5 6 5
  • B 3 7 6 5
  • C 1 2 2 3 5 1 3
  • D 6 0 2 3 5 6 5

Q3:

Simplify 913+7+9137.

  • A 3 7
  • B 3 1 3
  • C 3 1 3
  • D 3 7

Q4:

Given that 𝑥=306, 𝑦=216+3, and 𝑧=300+6, find the value of (𝑥𝑦+𝑧) expressing your answer in simplest form.

Q5:

What is the conjugate of 1211+43? Express your answer in simplest form.

  • A 4 3
  • B 2 1 1 + 4 3
  • C 4 3 2 1 1
  • D 2 1 1 4 3
  • E 2 1 1

Q6:

Given that 𝑎=957 and 𝑎=29, find the value of 𝑎.

  • A 9 5 7 + 2 9
  • B 3 3 2 9
  • C 9 5 7 2 9
  • D 9 5 7 2 9

Q7:

Given that 𝑥=25+227 and 𝑦=53242, find the value of 𝑥+𝑦.

  • A 1 1 3 8 4
  • B 5 2 1
  • C 4 3 + 2 7 1 0
  • D 4 3
  • E 4 3 2 7 1 0

Q8:

Given that 𝑥=12+7 and 𝑦=192+112, express 𝑥 in terms of 𝑦.

  • A 𝑦
  • B 1 6 𝑦
  • C 𝑦 4
  • D 𝑦 1 6
  • E 4 𝑦

Q9:

Simplify 201920+1920+192019.

  • A 8 9 5
  • B 7 8
  • C 8 9 5
  • D78

Q10:

Given that 𝑥=713 and 𝑦=137, find 182(𝑥+𝑦) expressing your answer in simplest form.

  • A 2 0 9 1
  • B 4 0 9 1
  • C 1 8 2 9 1
  • D 2 9 1
  • E 1 8 2 7 + 1 8 2 1 3

Q11:

Express 216611 in its simplest form.

  • A 6 6
  • B 2 1 6
  • C 1 1
  • D 6
  • E 2 1 1 1

Q12:

Simplify 207 by rationalizing the denominator.

  • A 2 0 7
  • B 2 0 7 4 9
  • C 2 0 7 4 9
  • D 2 0 7

Q13:

Simplify 93+10113 by rationalizing the denominator.

  • A 1 9 3 3 3
  • B 3 7 3 3
  • C 9 + 1 0 3 1 1
  • D 2 7 + 1 0 3 3 3

Q14:

Given that 𝑥=253 and 𝑦=53, find 𝑥+𝑦 expressing your answer in simplest form.

  • A20
  • B60
  • C 2 5
  • D12
  • E 2 3

Q15:

Given that 4727=𝑎2+𝑏, find the values of 𝑎 and 𝑏.

  • A 𝑎 = 1 , 𝑏 = 7
  • B 𝑎 = 1 , 𝑏 = 7
  • C 𝑎 = 7 , 𝑏 = 1
  • D 𝑎 = 1 , 𝑏 = 7

Q16:

Given that 6762+5=𝑎2+𝑏5, find the values of 𝑎 and 𝑏.

  • A 𝑎 = 1 , 𝑏 = 6
  • B 𝑎 = 6 , 𝑏 = 1
  • C 𝑎 = 6 , 𝑏 = 1
  • D 𝑎 = 6 , 𝑏 = 1

Q17:

Given that 7674481=𝑎+𝑏3, find the values of 𝑎 and 𝑏.

  • A 𝑎 = 1 , 𝑏 = 1 6
  • B 𝑎 = 1 , 𝑏 = 1 6
  • C 𝑎 = 1 , 𝑏 = 1 6
  • D 𝑎 = 1 6 , 𝑏 = 1

Q18:

Simplify 11182 by rationalizing the denominator.

  • A 1 1 2 3 6
  • B 1 1 2 1 8
  • C 1 8 2 1 1
  • D 1 1 2 3 6

Q19:

Simplify 6+767 by rationalizing the denominator.

  • A 1 2 9 4 3 1 2 7
  • B 1 2 9 4 3 + 1 2 7
  • C 4 3 1 2 7
  • D 4 3 + 1 2 7
  • E 1 4 3 2 9 + 1 2 7

Q20:

Simplify 3626 by rationalizing the denominator.

  • A 9 2 6
  • B 3 6 2 + 6
  • C 9 2 + 6
  • D 3 6 2 6
  • E 2 + 6

Q21:

Given that 𝑥=572 and 𝑦=72, find 𝑥𝑦 expressing your answer in simplest form.

  • A28
  • B56
  • C8
  • D 4 1 4

Q22:

Simplify 41037410 by rationalizing the denominator.

  • A 2 1 + 4 7 0 2 8
  • B 4 0 3 7 0 4 0
  • C 4 0 3 7 0 1 0
  • D 1 6 0 1 2 7 0 1 6 0
  • E 1 6 0 + 1 2 7 0 1 6 0

Q23:

Express 45+10515+5533 in its simplest form.

  • A 1 2 1 5 + 6 5
  • B 2 1 5
  • C 1 2 5
  • D 1 2 3
  • E 1 2 1 5

Q24:

Express 875648+512+448 in its simplest form.

  • A 7
  • B 9 7
  • C 9 7
  • D 7

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