Lesson Worksheet: Adding and Subtracting Square Roots Mathematics • 10th Grade

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In this worksheet, we will practice adding and subtracting square roots and practice using that to simplify expressions.

Q1:

Simplify −2+√6+8−√6.

Q2:

Simplify −7−√7+6+4√7.

  • A2+√7
  • B−1−5√7
  • C−1+3√7
  • D−1−√7

Q3:

Given that 𝑎=6−7√3 and 𝑏=−7−7√3, find the value of 𝑎+𝑏.

  • A−1−7√3
  • B−1
  • C−15+√3
  • D−1−14√3

Q4:

Given that 𝑎=√2+9 and 𝑏=√2−9, find the value of 𝑎−𝑏.

Q5:

Simplify √123+√123+√123.

  • A3√123
  • B√369
  • C√126
  • D√123

Q6:

Simplify 12√5+3√5.

  • A36√5
  • B15√5
  • C15√5
  • D15√10
  • E180

Q7:

Write √8+√2 in the form 𝑎√2, where 𝑎 is an integer.

  • A7√2
  • B4√2
  • C3√2
  • D5√2
  • E2√2

Q8:

Simplify √12−2√3+4√27.

  • A12√3
  • B7√3
  • C3√3
  • D11√3
  • E16√3

Q9:

Given that 9√8+10√50=𝑥√2, find the value of 𝑥.

Q10:

Express √75+√28−√27 in its simplest form.

  • A8√3+2√7
  • B2√3+2√7
  • C4√10
  • D4√3
  • E8√3−2√7

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