Lesson Worksheet: Rationalizing Denominators Mathematics • 10th Grade

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

Q1:

Simplify −1118√2 by rationalizing the denominator.

  • A−11√236
  • B−11√218
  • C−18√211
  • D11√236

Q2:

Simplify 4√10−3√74√10 by rationalizing the denominator.

  • A−21+4√7028
  • B40−3√7040
  • C40−3√7010
  • D160−12√70160
  • E160+12√70160

Q3:

Given that 𝑥=2√5+√22√7 and 𝑦=√5−3√2√42, find the value of 𝑥+𝑦.

  • A11384
  • B521
  • C43+27√10
  • D43
  • E43−27√10

Q4:

What is the conjugate of 11+94√94? Express your answer in simplest form.

  • A√94
  • B√94−11
  • C11+√94
  • D11−√94
  • E94√94

Q5:

Given that −47√2−7=𝑎√2+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 −36√2−√6 by rationalizing the denominator.

  • A9√2−√6
  • B−36√2+√6
  • C9√2+√6
  • D−36√2−√6
  • E√2+√6

Q7:

Given that 676√2+√5=𝑎√2+𝑏√5, 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=1√3−√2 and 𝑦=√3−√2, find (𝑥−𝑦).

Q9:

Given that 𝑥=522√19−2√6, and 𝑦 is the conjugate of 𝑥, find the value of 𝑥𝑦.

Q10:

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

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