Topic Details (Notes format)

How to Simplify Surds (Irrational Square Roots)

Subject: Mathematics

Book: Maths Mastery

“Surd” often refers to an irrational root that can’t be simplified to a rational number, like √2 or √7. We can simplify √18 to 3√2 by factoring out perfect squares. To add or subtract surds, they must share the same radicand: for instance, 2√3 + 3√3 = 5√3. Rationalizing denominators (like 1/√3 becoming √3/3) is key to presenting surd answers in standard form. Surd arithmetic underlies advanced algebra, geometry with exact distances, and calculations where approximations can degrade precision. Familiarity ensures you handle irrational values with exactness and clarity.

Practice Questions

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

View Question

If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

View Question

If a+b = 10 and ab = 21, what is the value of (a-b)^2?

View Question

If the sum of three consecutive integers is 72, what are the integers?

View Question

What is the probability of drawing an ace from a standard deck of 52 cards?

View Question

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

View Question

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

View Question

How many diagonals does a pentagon have?

View Question

If a square has a perimeter of 64 cm, what is its area?

View Question

What is the sum of all even numbers between 1 and 100?

View Question