Worksheet: Multiplying Radical Expressions

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In this worksheet, we will practice multiplying radicals (or surds) and using that to simplify expressions.

Q1:

Express 5√10+3√35√10−3√3 in its simplest form.

Q2:

Simplify 5√7(1+√7).

  • A12
  • B 5 √ 7 + 5
  • C 5 √ 7 + 3 5
  • D 6 √ 7

Q3:

Simplify √2+9−5+√2.

  • A14
  • B − 4 5
  • C 4 √ 2 − 4 3
  • D 2 √ 2 + 4
  • E − 4 3 √ 2 + 4

Q4:

Simplify √6−3−√6−3−6+√6.

  • A − 3 √ 6 + 1 8
  • B − 6 √ 6 + 2 4
  • C − 7 √ 6 + 1 8
  • D − 6 √ 6 + 1 2

Q5:

Express √1511√5+2√3 in its simplest form.

  • A 5 5 √ 3 + 6 √ 5
  • B 5 √ 3 + 3 √ 5
  • C195
  • D 3 3 √ 3 + 1 5 √ 5
  • E 6 1 √ 1 5

Q6:

Express 10+√17+75 in its simplest form.

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

Q7:

Express √7+√3−√84 in its simplest form.

  • A 1 0 + √ 8 4
  • B 1 0 − 2 √ 2 1
  • C √ 7 + √ 3
  • D 1 0 + 2 √ 2 1
  • E10

Q8:

Find the value of √21+√13√21−√13.

  • A − 6 4
  • B 1 6 4
  • C − 1 6 4
  • D64

Q9:

Simplify √7+6−7+√7.

  • A − 3 5 √ 7 − 1
  • B − 4 2
  • C13
  • D 2 √ 7 − 1
  • E − √ 7 − 3 5

Q10:

Simplify √7−97+√7.

  • A − 2 √ 7 − 5 6
  • B − 1 6
  • C 2 √ 7 − 2
  • D − 6 3
  • E − 5 6 √ 7 − 2

Q11:

Simplify √7−6−8+√7.

  • A2
  • B 5 5 √ 7 − 1 4
  • C48
  • D 2 √ 7 − 1 4
  • E − 1 4 √ 7 + 5 5

Q12:

Simplify √5−3−√5−7−4+√5.

  • A − 3 √ 5 + 2 8
  • B − 1 0 √ 5 + 3 3
  • C − 1 1 √ 5 + 2 8
  • D − 1 0 √ 5 + 2 3

Q13:

Express √107√2+√5 in its simplest form.

  • A 1 4 √ 5 + 5 √ 2
  • B 2 √ 5 + 5 √ 2
  • C80
  • D 3 5 √ 5 + 1 0 √ 2
  • E 1 9 √ 1 0

Q14:

Express 12√6+8√212√6−8√2 in its simplest form.

Q15:

Simplify 8√7(−1−√7).

  • A − 1 5
  • B − √ 7 + 8
  • C − 8 √ 7 − 5 6
  • D − 9 √ 7

Q16:

Simplify −6√5(−7+√5).

  • A47
  • B − 6 √ 5 + 4 2
  • C 4 2 √ 5 − 3 0
  • D 4 3 √ 5

Q17:

Given that 𝑥16+√2=16−√2, find the value of 𝑥 stating your answer in simplest form.

Q18:

Express 3√8×2√2 in its simplest form.

Q19:

Express 4√2×√48 in its simplest form.

  • A 2 4 √ 2
  • B24
  • C 1 6 √ 6
  • D384

Q20:

Calculate √53×√53.

Q21:

Calculate 12√3×7√3.

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