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
  • B5√7+5
  • C5√7+35
  • D6√7

Q3:

Simplify √2+9−5+√2.

  • A−45
  • B−43√2+4
  • C4√2−43
  • D2√2+4
  • E14

Q4:

Simplify √6−3−√6−3−6+√6.

  • A−3√6+18
  • B−6√6+24
  • C−7√6+18
  • D−6√6+12

Q5:

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

  • A55√3+6√5
  • B5√3+3√5
  • C195
  • D33√3+15√5
  • E61√15

Q6:

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

  • A192+2√17
  • B192+10√17
  • C192+20√17
  • D102+20√17

Q7:

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

Q8:

Find the value of √21+√13√21−√13.

Q9:

Simplify √7+6−7+√7.

  • A−42
  • B−35√7−1
  • C−√7−35
  • D2√7−1
  • E13

Q10:

Simplify √7−97+√7.

  • A−63
  • B−56√7−2
  • C−2√7−56
  • D2√7−2
  • E−16

Q11:

Simplify √7−6−8+√7.

  • A48
  • B55√7−14
  • C−14√7+55
  • D2√7−14
  • E2

Q12:

Simplify √5−3−√5−7−4+√5.

  • A−3√5+28
  • B−10√5+33
  • C−11√5+28
  • D−10√5+23

Q13:

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

  • A14√5+5√2
  • B2√5+5√2
  • C80
  • D35√5+10√2
  • E19√10

Q14:

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

Q15:

Simplify 8√7(−1−√7).

  • A−15
  • B−√7+8
  • C−8√7−56
  • D−9√7

Q16:

Simplify −6√5(−7+√5).

  • A47
  • B−6√5+42
  • C42√5−30
  • D43√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.

  • A24√2
  • B24
  • C16√6
  • D384

Q20:

Calculate √53×√53.

Q21:

Calculate 12√3×7√3.

Q22:

Express 5944×4459 in its simplest form.

Q23:

Expand and simplify the expression √5−√72√7+3√5.

  • A3√5−2√7−√35
  • B2√7−√35
  • C−√35
  • D−2√7−√35
  • E1−√35

Q24:

What is the value of √7×√8?

Q25:

Express √4×√−16 in its simplest form.

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