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Lesson: Operations on Real Numbers

In this lesson, we will learn how to solve problems involving operations and properties of operations on real numbers.

Sample Question Videos

02:34

Worksheet • 15 Questions • 1 Video

Q1:

Given that the dimensions of a rectangle are 1 2 + √ 2 cm and 1 2 − √ 2 cm, find its area.

Q2:

Find the multiplicative inverse of √ 6 3 0 .

  • A 5 √ 6
  • B − 3 0 √ 6
  • C 3 0 √ 6
  • D − 5 √ 6
  • E − √ 6 3 0

Q3:

Given that 𝑎 √ 3 is the multiplicative inverse of 1 √ 3 , find the value of 𝑎 .

Q4:

What is the additive inverse of 9 1 √ 1 7 ?

  • A − 9 1 √ 1 7 1 7
  • B 9 1 √ 1 7 1 7
  • C 1 7 √ 1 7 9 1
  • D − 1 7 √ 1 7 9 1

Q5:

Find the multiplicative inverse of √ 6 + √ 7 expressing your answer in simplest form.

  • A √ 7 − √ 6
  • B √ 6 − √ 7
  • C 1 √ 6 − √ 7
  • D 1 √ 7 − √ 6

Q6:

Given that 𝑎 5 is the multiplicative inverse of √ 5 1 1 , find the value of 𝑎 .

  • A 1 1 √ 5
  • B 1 1 √ 5
  • C − √ 5 1 1
  • D √ 5
  • E − 1 1 √ 5

Q7:

Given that the multiplicative inverse of √ 𝑎 + 2 is √ 𝑎 − 2 1 0 , find the value of 𝑎 .

Q8:

Complete √ 3 + 1 2 = 1 2 + .

  • A √ 3
  • B − √ 3
  • C − √ 1 5
  • D √ 1 5

Q9:

Complete √ 2 + 1 3 = 1 3 + .

  • A √ 2
  • B − √ 2
  • C − √ 1 5
  • D √ 1 5

Q10:

What is the additive inverse of √ 6 5 − √ 8 5 ?

  • A √ 8 5 − √ 6 5
  • B − √ 8 5 − √ 6 5
  • C √ 6 5 − √ 8 5
  • D √ 6 5 + √ 8 5

Q11:

Find the multiplicative inverse of 1 2 √ 1 4 .

  • A √ 1 4 1 2
  • B √ 1 2 1 4
  • C − 1 2 √ 1 4
  • D 1 4 √ 1 2

Q12:

Find the multiplicative inverse of √ 0 . 3 6 , giving your answer in its simplest form.

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

Q13:

Find the additive inverse of 8 − √ 1 3 5 .

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

Q14:

Which of the following equations illustrates the multiplicative inverse property?

  • A 𝑥 1 𝑥 = 1
  • B 𝑥 ⋅ 0 = 0
  • C 𝑥 + ( 𝑏 + 𝑐 ) = ( 𝑥 + 𝑏 ) + 𝑐
  • D 𝑥 + 𝑏 = 𝑏 + 𝑥
  • E 𝑥 ( 𝑏 + 𝑐 ) = 𝑥 𝑏 + 𝑥 𝑐

Q15:

Given that 𝑥 = √ 1 1 2 √ 8 , find 𝑥 − 1 .

  • A √ 1 4 1 4
  • B 8 √ 1 4
  • C √ 1 4
  • D 2 √ 2
  • E √ 2 4
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