Worksheet: Simplifying Radicals

In this worksheet, we will practice performing mathematical operations on radicals and utilizing the conjugate to rationalize the denominator of a radical and simplifying radical expressions.

Q1:

Given that ๐‘ฅ<0, simplify โˆš๐‘ฅโˆ’โˆš๐‘ฅโˆ’โˆš๐‘ฅโˆ’2๐‘ฅ+1+1=๏Šจ๏Šฉ๏Šจ๏Žข.

  • Aโˆ’๐‘ฅ
  • B0
  • C๐‘ฅ
  • Dโˆ’1

Q2:

Simplify 5โˆš50.

  • A10โˆš2
  • B25โˆš2
  • C10โˆš25
  • D125โˆš2
  • E5โˆš50

Q3:

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

Q4:

Calculate ๏„6ร—โˆš49รทโˆš8+2๏Žข๏Šจ.

Q5:

If ๐‘ฅ=4โˆš10 and ๐‘ฆ=6โˆš3, is it true that โˆš๐‘ฅโˆ’๐‘ฆโˆ’7=3๏Šจ๏Šช?

  • Ano
  • Byes

Q6:

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

Q7:

Given that ๐‘ฅ=โˆš22, ๐‘ฆ=1โˆš5, and ๐‘ง=โˆš64, find the value of ๐‘ฅ+(๐‘ฅ๐‘ฆ๐‘ง)๏Šจ๏Šจ.

  • A380
  • B4340
  • C4380
  • D43160

Q8:

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

Q9:

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

  • A915
  • B285
  • C525
  • D1015

Q10:

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

  • A1
  • B2
  • C10
  • D109

Q11:

Find the value of ๏Žฆ๏„(โˆ’128)๏Šจ.

Q12:

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

Q13:

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

Q14:

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

  • A1
  • B56
  • Cโˆš6โˆš5
  • D65
  • E6โˆš65โˆš5

Q15:

Given that ๏„ž๐‘Ž๐‘=โˆš๐‘Žโˆš๐‘, simplify ๏„ž121๐‘ฅ๏Šญ๏Šฆ.

  • A121|๐‘ฅ|๏Šฉ๏Šซ
  • B||๐‘ฅ||121๏Šฉ๏Šซ
  • C11|๐‘ฅ|๏Šฉ๏Šซ
  • D๐‘ฅ11๏Šญ๏Šฆ
  • E11๐‘ฅ๏Šญ๏Šฆ

Q16:

Simplify ๏Žขโˆšโˆ’0.064๐‘Ž๏Šฉ๏Šฆ.

  • Aโˆ’0.064๐‘Ž๏Šง๏Šฆ
  • B0.4๐‘Ž๏Šง๏Šฆ
  • Cโˆ’0.4๐‘Ž๏Šฉ๏Šฆ
  • Dโˆ’0.4๐‘Ž๏Šง๏Šฆ
  • E0.04๐‘Ž๏Šง๏Šฆ

Q17:

Simplify โˆš486ร—๏€ปโˆš42๏‡๏€ปโˆš7๏‡๏Šฑ๏Šซ๏Šฑ๏Šซ.

  • A14
  • B๏€ปโˆš6๏‡ร—๏€ปโˆš7๏‡๏Šฑ๏Šซ๏Šฑ๏Šง๏Šฆ
  • C54
  • D136

Q18:

Solve ๏€ป4โˆš6+6๏‡=132+๐‘Ž๏Šจ.

  • A๐‘Ž=48
  • B๐‘Ž=8โˆš6
  • C๐‘Ž=24โˆš6
  • D๐‘Ž=48โˆš6
  • E๐‘Ž=4โˆš6

Q19:

Express 52โˆš252 in the form ๐‘Žโˆš๐‘ where ๐‘Ž and ๐‘ are integers and ๐‘ takes the least possible value.

  • A15โˆš7
  • B6โˆš7
  • C52โˆš7
  • D45โˆš7
  • E90โˆš7

Q20:

Find the conjugate of 6โˆš7+โˆš3, then find the product of 6โˆš7+โˆš3 and its conjugate.

  • A16โˆš7+โˆš3, 249
  • B6โˆš7โˆ’โˆš3, 249
  • C16โˆš7+โˆš3, 1
  • D16โˆš7+โˆš3, 126
  • E6โˆš7โˆ’โˆš3, 255

Q21:

Calculate โˆš18รท6+17โˆ’(33โˆ’29).

Q22:

What is the value of ๏€ปโˆš7รทโˆš6๏‡๏Šจ?

  • A4936
  • B76
  • Cโˆš7โˆš6
  • D67

Q23:

Which of the following is equal to ๏„(๐‘ฅ+๐‘ฆ)๏Šซ๏Šฎ?

  • Aโˆ’(๐‘ฅ+๐‘ฆ)
  • B||(๐‘ฅ+๐‘ฆ)||๏Šจ๏Šฏ
  • C|(๐‘ฅ+๐‘ฆ)|
  • D(๐‘ฅ+๐‘ฆ)๏Šซ๏Šฌ
  • Eโˆ’(๐‘ฅ+๐‘ฆ)๏Šจ๏Šฏ

Q24:

What is the value of ๏€ฟ1โˆš2๏‹รท๏€ฟ1โˆš2๏‹๏Šจ๏Šฎ?

  • A8โˆš2
  • Bโˆš28
  • C8
  • D18

Q25:

Is the cube root of a negative number positive or negative?

  • Apositive
  • Bnegative

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