Topic Details (Notes format)

How to Simplify Radicals (Square Roots)

Subject: Mathematics

Book: Maths Mastery

Radical simplification often involves extracting perfect squares from under the radical sign. For √72, note 72 = 36 × 2, so √72 = √(36×2) = √36 × √2 = 6√2. More complex operations can include rationalizing denominators, e.g., 1 / √5 can be written as √5 / 5 by multiplying numerator and denominator by √5. Proficiency with radicals appears in geometry (Pythagorean distances), advanced algebra, and real-world measurements requiring root approximations. Frequent practice with factorization and rationalization ensures you handle square roots, cube roots, or higher-order radicals with confidence.

Practice Questions

What is the greatest common divisor (GCD) of 36 and 48?

View Question

How many diagonals does a pentagon have?

View Question

If 2a + b = 10 and a - b = 4, what is the value of a?

View Question

If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

View Question

A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

View Question

What is the HCF of 72 and 120?

View Question

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

View Question

What is the sum of all odd numbers from 1 to 99?

View Question

If x + 1/x = 5, what is the value of x^2 + 1/x^2?

View Question

If 5x - 2 = 13, what is the value of x?

View Question