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Lesson: Operations with Square Roots

Sample Question Videos

Worksheet • 25 Questions • 2 Videos

Q1:

Expand 6 7 2 .

  • A 5 5 1 4 6
  • B 55
  • C 5 5 7 6
  • D 5 5 + 1 4 6

Q2:

Express 1 2 8 + 1 8 8 1 2 in its simplest form.

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

Q3:

Simplify 5 × 5 by combining similar terms.

  • A 5 2
  • B 2 5
  • C 2 5
  • D ( 2 ) 5
  • E 5 4

Q4:

Express ( 3 ) + 4 0 5 5 5 5 2 in its simplest form.

  • A 3 2 5
  • B 3 2 5
  • C 3 + 2 0 5
  • D 3 + 3 3 5
  • E 2 + 3 5

Q5:

Simplify 3 9 5 3 + 9 3 5 3 .

  • A 4 4 1 5
  • B 4 4 5
  • C 1 3 2 1 0 3
  • D 1 3 2 1 5
  • E 1 3 2 3 5

Q6:

Calculate 1 1 + 1 2 4 9 1 9 6 .

Q7:

Calculate 1 4 + 2 5 1 6 7 6 2 0 .

  • A 5 1 6
  • B 1 8
  • C 1 4
  • D 1 7 6 0
  • E 2 1 1 6

Q8:

Calculate 2 5 + 1 4 4 4 9 .

  • A 1 3 7
  • B 1 7 7
  • C 5 7
  • D 1 0 7
  • E 1 2 7

Q9:

Given that 𝑥 = 3 + 7 , find the value of 𝑥 + 4 𝑥 + 4 4 2 .

  • A 3 2 + 1 0 7
  • B70
  • C 1 2 + 1 0 7
  • D102
  • E 3 2 + 5 7

Q10:

Given that 𝑥 = 1 6 5 and 𝑦 = 6 5 , find ( 𝑥 + 𝑦 ) 2 .

Q11:

What is the conjugate of 1 1 + 9 4 9 4 ? Express your answer in simplest form.

  • A 1 1 9 4
  • B 9 4 9 4
  • C 1 1 + 9 4
  • D 9 4
  • E 9 4 1 1

Q12:

Given that 𝑥 = 1 5 2 1 2 2 5 , evaluate 𝑥 3 2 .

Q13:

Simplify 1 1 3 1 3 5 + 1 5 7 1 7 9 + 1 9 1 1 .

  • A 1 1 1 2
  • B 1 + 1 1
  • C 1 + 1 1 2
  • D 1 + 1 1
  • E 1 1 1 2

Q14:

Given that 𝑎 = 5 4 and 𝑏 = 2 5 8 1 , find 𝑎 𝑏 .

  • A 5 6
  • B 1 0 1 3
  • C 5 1 8
  • D 2 5 1 3

Q15:

A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. The Pythagorean theorem can be used to find the length of the guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 9 0 0 0 0 feet. The square of the height of the pylon is 1 6 0 0 0 0 feet. Therefore, the length of the guy wire can be found by evaluating 9 0 0 0 0 + 1 6 0 0 0 0 . What is its length?

Q16:

Calculate 1 3 1 2 3 .

  • A 1 3
  • B 1 2
  • C 4 5
  • D 2 3
  • E 3 5

Q17:

What is the conjugate of 𝑥 = 2 + 5 ? Find the product of 𝑥 and its conjugate.

  • A 2 5 , 3
  • B 1 2 + 5 , 1
  • C 2 5 , 7
  • D 1 2 + 5 , 3
  • E 1 2 + 5 , 1 0

Q18:

Calculate 1 6 9 × 1 2 0 .

  • A 1 1 5
  • B 4 3
  • C 5 2 3
  • D 1 1 2

Q19:

Given that 𝑥 = 2 2 , find the value of 𝑥 + 2 2 .

  • A 0 or 8
  • B 0 or 4
  • C 2 or 8
  • D 8 or 4

Q20:

Simplify 8 1 0 1 0 ÷ 6 3 7 .

  • A3
  • B 1 3
  • C 7 1 0
  • D 1 0 7

Q21:

Given that 𝑎 = 2 5 4 1 and 𝑏 = 4 1 2 5 , find 𝑎 𝑏 .

  • A 2 0 4 1
  • B 4 1 2 0
  • C 2 2 0 5
  • D1

Q22:

Write the following as a fraction in its simplest form: 6 4 1 2 1 2 .

  • A 6 4 1 2 1
  • B 8 1 2 1
  • C 8 1 1
  • D 1 2 1 6 4
  • E 1 2 8 1 2 1

Q23:

Express 4 0 3 0 0 3 0 in its simplest form.

  • A 1 0
  • B 3
  • C 3 1 0
  • D 3 0
  • E 2

Q24:

Calculate 4 × 8 1 × 4 × 8 1 .

Q25:

What is the conjugate of 2 7 ? What is the product of 2 7 and its conjugate?

  • A 2 + 7 , 3
  • B 1 2 7 , 1
  • C 2 + 7 , 1 1
  • D 1 2 7 , 3
  • E 1 2 7 , 1 4
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