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Worksheet: Multiplying Radical Expressions

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

Q1:

Simplify 5 √ 7 ( 1 + √ 7 ) .

  • A 5 √ 7 + 5
  • B 6 √ 7
  • C 12
  • D 5 √ 7 + 3 5

Q2:

Simplify 8 √ 7 ( − 1 − √ 7 ) .

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

Q3:

Simplify − 6 √ 5 ( − 7 + √ 5 ) .

  • A − 6 √ 5 + 4 2
  • B 4 3 √ 5
  • C 47
  • D 4 2 √ 5 − 3 0

Q4:

Simplify √ 2 + 9 − 5 + √ 2 .

  • A 2 √ 2 + 4
  • B − 4 3 √ 2 + 4
  • C14
  • D 4 √ 2 − 4 3
  • E − 4 5

Q5:

Simplify √ 7 + 6 − 7 + √ 7 .

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

Q6:

Simplify √ 7 − 9 7 + √ 7 .

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

Q7:

Simplify √ 7 − 6 − 8 + √ 7 .

  • A 2 √ 7 − 1 4
  • B 5 5 √ 7 − 1 4
  • C2
  • D − 1 4 √ 7 + 5 5
  • E48

Q8:

Simplify √ 6 − 3 − √ 6 − 3 − 6 + √ 6 .

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

Q9:

Simplify √ 5 − 3 − √ 5 − 7 − 4 + √ 5 .

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

Q10:

Express √ 1 5 1 1 √ 5 + 2 √ 3 in its simplest form.

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

Q11:

Express √ 1 0 7 √ 2 + √ 5 in its simplest form.

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

Q12:

Express 5 √ 1 0 + 3 √ 3 5 √ 1 0 − 3 √ 3 in its simplest form.

Q13:

Express 1 2 √ 6 + 8 √ 2 1 2 √ 6 − 8 √ 2 in its simplest form.

Q14:

Express √ 7 + √ 3 − √ 8 4 2 in its simplest form.

  • A 1 0 − 2 √ 2 1
  • B 1 0 + 2 √ 2 1
  • C √ 7 + √ 3
  • D10
  • E 1 0 + √ 8 4

Q15:

Express 1 0 + √ 1 7 + 7 5 2 in its simplest form.

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

Q16:

Find the value of √ 2 1 + √ 1 3 √ 2 1 − √ 1 3 2 2 .

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

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