Lesson Worksheet: Simplifying Radicals Mathematics

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In this worksheet, we will practice simplifying radicals and expressions involving radicals.

Q1:

Given that ๐‘Ž=โˆš3 and ๐‘=โˆš2, find the value of ๐‘Žโˆ’๐‘๏Šจ๏Šฌ.

Q2:

Calculate ๏„6ร—โˆš49รทโˆš8+2๏Žข๏Šจ.

Q3:

Simplify ๏Žฅโˆš(๐‘ฅ+6๐‘ฆ)๏Šฉ๏Šฌ.

  • A(๐‘ฅ+๐‘ฆ)
  • B(๐‘ฅ+๐‘ฆ)๏Šฌ
  • C(๐‘ฅ+6๐‘ฆ)
  • D(๐‘ฅ+6๐‘ฆ)๏Šฌ

Q4:

Given that ๐‘Ž=โˆš7 and ๐‘=๏€ปโˆš7๏‡๏Šฑ๏Šง, find the value of ๐‘Ž๐‘๏Šง๏Šซ๏Šง๏Šฌ.

  • A1โˆš7
  • B17
  • Cโˆš7
  • D1
  • E7

Q5:

Calculate ๏„Ÿ๏€ผ125๏ˆโˆ’16ร—๏€ผ125๏ˆ+64๏Šจ.

  • A915
  • B285
  • C525
  • D1015

Q6:

What is the value of 3+3๏€ฟโˆ’1โˆš3๏‹๏Šฆ๏Šฑ๏Šง๏Šจ?

  • A1
  • B2
  • C10
  • D109

Q7:

Find the value of ๏Žฆ๏„(โˆ’128)๏Šจ.

Q8:

Express โˆš640 in the form ๐‘Žโˆš๐‘ where ๐‘Ž and ๐‘ are integers and ๐‘ takes the least possible value.

  • A20โˆš2
  • B200โˆš2
  • C8โˆš10
  • D64โˆš10

Q9:

Express 3โˆš45 in the form ๐‘Žโˆš๐‘ where ๐‘Ž and ๐‘ are integers and ๐‘ takes the least possible value.

  • A9โˆš5
  • B3โˆš5
  • C13.5โˆš5
  • D27โˆš5

Q10:

What is the value of ๏€ฟ6โˆš55โˆš6๏‹๏Šจ?

  • A1
  • B56
  • Cโˆš6โˆš5
  • D65
  • E6โˆš65โˆš5

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