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

If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

View Question

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

View Question

If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

View Question

If the length of a rectangle is doubled and the width is halved, what is the change in area?

View Question

What is the slope of a line passing through the points (2, 3) and (4, 7)?

View Question

If x - y = 5 and x + y = 15, what is the value of x?

View Question

If 2x = 16, what is the value of x?

View Question

If the product of two numbers is 120 and their sum is 26, what are the numbers?

View Question

A sphere has a radius of 7 cm. What is its volume?

View Question

If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

View Question