Lesson: Operations with Radicals

In this lesson, we will learn how to perform mathematical operations on radicals and how to utilize the conjugate to rationalize the denominator of a radical.

Sample Question Videos

  • 07:13
  • 01:35

Worksheet: Operations with Radicals • 25 Questions • 2 Videos

Q1:

Express 3 3 2 5 6 4 in its simplest form.

Q2:

Express 3 3 3 7 2 + 7 2 9 1 8 1 6 5 7 6 in its simplest form.

Q3:

Given that 𝑥 = 4 1 5 4 + 1 5 and 𝑦 = 9 6 3 1 5 , determine the value of 𝑥 + 𝑦 expressing your answer in simplest form.

Q4:

Express 5 5 4 3 2 0 3 3 in its simplest form.

Q5:

Given that 𝑎 = 5 + 8 and 𝑏 = 5 8 , find the value of 𝑎 + 𝑏 .

Q6:

Simplify 2 4 8 + 1 0 6 1 3 .

Q7:

Given that 𝑎 = 5 + 7 and 𝑏 = 5 7 , find 𝑎 𝑏 .

Q8:

Express 1 1 2 + 2 0 2 + 5 × 1 0 in its simplest form.

Q9:

Given that 𝑥 = 1 2 + 1 0 1 0 and 𝑦 = 1 0 1 2 1 0 , find 𝑥 𝑦 expressing your answer in simplest form.

Q10:

Express 3 3 3 5 ÷ 2 5 9 in its simplest form.

Q11:

What is the value of 2 ÷ 2 2 + 3 6 × 6 5 ?

Q12:

Given that 𝑥 = 1 3 2 and 𝑦 = 3 2 , find ( 𝑥 𝑦 ) 2 .

Q13:

Given that 𝑥 = 2 3 and 𝑦 = 2 + 3 , find 𝑥 + 𝑦 𝑥 𝑦 1 expressing your answer in simplest form.

Q14:

Given that 𝑥 = 7 + 5 and 𝑦 = 2 𝑥 , find 𝑥 + 𝑦 𝑥 𝑦 expressing your answer in simplest form.

Q15:

Given that 𝑥 = 1 4 2 + 1 7 and 𝑦 = 1 4 2 1 7 , find ( 𝑥 + 𝑦 ) 2 .

Q16:

Given that 𝑥 = 3 and 𝑦 = 6 , find the value of 𝑥 + 𝑦 𝑥 𝑦 2 .

Q17:

Given that 𝑎 = 6 4 and 𝑏 = 6 4 , find the value of 𝑎 + 𝑏 .

Q18:

Given that 𝑎 = 6 6 + 1 and 𝑏 = 6 6 1 , find the value of 𝑎 + 𝑏 2 2 .

Q19:

Calculate 2 2 × 4 7 1 1 ÷ 8 2 7 7 .

Q20:

Express 4 3 2 + 1 5 1 5 4 5 6 1 2 in its simplest form.

Q21:

Evaluate 1 0 0 2 1 6 3 .

Q22:

Determine the value of 5 1 6 2 5 1 1 3 9 1 2 5 1 4 3 3 3 3 .

Q23:

Express 5 6 9 6 + 4 6 + 6 3 3 in its simplest form.

Q24:

Find the value of 4 7 5 + 4 7 5 2 3 3 .

Q25:

Given that 𝑥 = 7 6 and 𝑦 = 7 + 6 , find the value of 𝑥 𝑦 𝑦 ( 𝑥 + 𝑦 ) 8 9 2 .

Preview

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.