Lesson Worksheet: Rationalizing Denominators Mathematics • 10th Grade

In this worksheet, we will practice rationalizing ‌square‌ ‌roots‌ ‌in‌ ‌the‌ ‌denominators‌ ‌of‌ ‌fractions.‌

Q1:

Simplify 11182 by rationalizing the denominator.

  • A11236
  • B11218
  • C18211
  • D11236

Q2:

Simplify 41037410 by rationalizing the denominator.

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

Q3:

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

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

Q4:

What is the conjugate of 11+9494? Express your answer in simplest form.

  • A94
  • B9411
  • C11+94
  • D1194
  • E9494

Q5:

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

Q6:

Simplify 3626 by rationalizing the denominator.

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

Q7:

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

Q8:

Given that 𝑥=132 and 𝑦=32, find (𝑥𝑦).

Q9:

Given that 𝑥=5221926, and 𝑦 is the conjugate of 𝑥, find the value of 𝑥𝑦.

Q10:

Given that 𝑥=133 and 𝑦=13+3, find the value of 𝑥𝑦+𝑦𝑥.

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