Surds (Higher Tier)

Surds (Higher Tier)

Understanding Surds

• A surd is essentially a square root that isn’t a whole number. Surds are irrational numbers, meaning they cannot be represented as a fraction.
• The symbol √ is called a radical sign. It indicates the square root of a number. For example, √9 = 3.

Simplifying Surds

• When simplifying surds, look for a perfect square factor within the surd. For instance, √50 can be simplified into 5√2 because 50=25*2 and √25=5.
• Remember, √a x √a = a. Utilize this property in simplifying expressions with surds.
• When simplifying surds in fraction form, it is often necessary to rationalise the denominator. This can be done by multiplying the fraction by the conjugate of the denominator.

Working with Surds

• Surds can be added or subtracted if they’re the same. For example, √3 + 2√3 = 3√3.
• Remember the rule of multiplication for surds - √a x √b = √(a x b).
• The division rule for surds states - √a / √b = √(a / b).

Key Concepts in Surds

• Always keep in mind that surds are irrational numbers. They cannot be exactly expressed as fractions.
• The square root of a number is a value which, when multiplied by itself, gives the original number.
• Grasp the principle of rationalising the denominator and how it helps in simplifying fractions with surds.

Common Pitfalls in Surds

• Students often forget to simplify surds by finding perfect square factors.
• Be wary that adding and subtracting surds requires identical surds. For instance, √3 and 2√3 can be added, but √3 and √5 cannot.
• Keep an eye out for negative surds. While it’s common to say the square root of a negative number is an imaginary number, in reality, this isn’t entirely accurate.