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

Please verify your account before proceeding.

In this lesson, we will learn how to solve problems on the operations of the square roots and how to find the conjugates of radical expressions and their product.

Q1:

Expand √ 6 − 7 2 .

Q2:

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

Q3:

Simplify − √ 5 × − √ 5 by combining similar terms.

Q4:

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

Q5:

Simplify 3 9 5 3 + 9 3 5 3 .

Q6:

Calculate 1 1 + 1 2 √ 4 9 − √ 1 9 6 .

Q7:

Calculate 1 4 + 2 5 1 6 − 7 6 2 0 .

Q8:

Calculate 2 5 + 1 4 4 4 9 .

Q9:

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

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.

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 .

Q14:

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

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 .

Q17:

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

Q18:

Calculate 1 6 9 × 1 2 0 .

Q19:

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

Q20:

Simplify √ 8 1 0 √ 1 0 ÷ √ 6 3 √ 7 .

Q21:

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

Q22:

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

Q23:

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

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?

Don’t have an account? Sign Up