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
  • C27
  • D8
  • E22

Q2:

Simplify 12523135 by rationalizing the denominator.

  • A11565
  • B3765
  • C1223513
  • D6023565

Q3:

Simplify 913+7+9137.

  • A37
  • B313
  • C313
  • D37

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.

  • A43
  • B211+43
  • C43211
  • D21143
  • E211

Q6:

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

  • A957+29
  • B3329
  • C95729
  • D95729

Q7:

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

  • A11384
  • B521
  • C43+2710
  • D43
  • E432710

Q8:

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

  • A𝑦
  • B16𝑦
  • C𝑦4
  • D𝑦16
  • E4𝑦

Q9:

Simplify 201920+1920+192019.

  • A895
  • B78
  • C895
  • D78

Q10:

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

  • A2091
  • B4091
  • C18291
  • D291
  • E1827+18213

Q11:

Express 216611 in its simplest form.

  • A66
  • B216
  • C11
  • D6
  • E2111

Q12:

Simplify 207 by rationalizing the denominator.

  • A207
  • B20749
  • C20749
  • D207

Q13:

Simplify 93+10113 by rationalizing the denominator.

  • A19333
  • B3733
  • C9+10311
  • D27+10333

Q14:

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

  • A20
  • B60
  • C25
  • D12
  • E23

Q15:

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

  • A𝑎=1, 𝑏=7
  • B𝑎=1, 𝑏=7
  • C𝑎=7, 𝑏=1
  • D𝑎=1, 𝑏=7

Q16:

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

  • A𝑎=1, 𝑏=6
  • B𝑎=6, 𝑏=1
  • C𝑎=6, 𝑏=1
  • D𝑎=6, 𝑏=1

Q17:

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

  • A𝑎=1, 𝑏=16
  • B𝑎=1, 𝑏=16
  • C𝑎=1, 𝑏=16
  • D𝑎=16, 𝑏=1

Q18:

Simplify 11182 by rationalizing the denominator.

  • A11236
  • B11218
  • C18211
  • D11236

Q19:

Simplify 6+767 by rationalizing the denominator.

  • A12943127
  • B12943+127
  • C43127
  • D43+127
  • E14329+127

Q20:

Simplify 3626 by rationalizing the denominator.

  • A926
  • B362+6
  • C92+6
  • D3626
  • E2+6

Q21:

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

  • A28
  • B56
  • C8
  • D414

Q22:

Simplify 41037410 by rationalizing the denominator.

  • A21+47028
  • B4037040
  • C4037010
  • D1601270160
  • E160+1270160

Q23:

Express 45+10515+5533 in its simplest form.

  • A1215+65
  • B215
  • C125
  • D123
  • E1215

Q24:

Express 875648+512+448 in its simplest form.

  • A7
  • B97
  • C97
  • D7

Q25:

Given that 𝑥=165 and 𝑦=65, find (𝑥+𝑦).

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