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Dec 29, 2025

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2 pages

Understanding and Working with Surds

Leah Strawbridge

@leahstrawbridge_kjnx

Surds are square roots that can't be simplified into whole... Show more

$a surd is a square root which cannot be reduced to a rational number (integer or Haction). $ \sqrt{2}$ is a surd $ \sqrt{5}$ is a surd $ \s$

What Are Surds?

Ever wondered why some square roots just won't turn into neat numbers? That's exactly what surds are - square roots that refuse to become rational numbers (whole numbers or fractions).

Take √2 or √5 - these are perfect examples of surds because they can't be simplified further. However, √81 might look like a surd at first glance, but it actually equals 9, so it's not a real surd.

The key to simplifying surds is hunting for square number factors. For example, with √20, you'd spot that 4 is a factor of 20 and 4 is a perfect square. This means √20 = √(4 × 5) = √4 × √5 = 2√5.

Quick Tip: Always look for the largest square number that divides into your number - it'll save you time and effort!

$a surd is a square root which cannot be reduced to a rational number (integer or Haction). $ \sqrt{2}$ is a surd $ \sqrt{5}$ is a surd $ \s$

Adding, Subtracting and Multiplying Surds

Adding and subtracting surds follows a simple rule: the surd parts must match! Think of it like collecting like terms in algebra. 4√3 + 5√3 = 9√3 because both terms have √3.

When the surds don't match initially, like √48 + √27, you'll need to simplify first. √48 becomes 4√3 and √27 becomes 3√3, giving you 4√3 + 3√3 = 7√3. Subtraction works exactly the same way: 6√5 - 2√5 = 4√5.

Multiplying surds is actually quite straightforward. You can multiply the numbers under the square root signs together: √2 × √98 = √196 = 14. When you have coefficients (numbers in front), multiply those separately: 3√2 × 5√3 = 15√6.

Remember: √a × √b = √(a × b) - this rule will be your best friend in surd calculations!

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478

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Dec 29, 2025

•

2 pages

Understanding and Working with Surds

Leah Strawbridge

@leahstrawbridge_kjnx

Surds are square roots that can't be simplified into whole numbers or fractions - they're really useful in maths when you need exact answers rather than decimals. Don't worry, they're not as scary as they look, and once you get... Show more

$a surd is a square root which cannot be reduced to a rational number (integer or Haction). $ \sqrt{2}$ is a surd $ \sqrt{5}$ is a surd $ \s$

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What Are Surds?

Ever wondered why some square roots just won't turn into neat numbers? That's exactly what surds are - square roots that refuse to become rational numbers (whole numbers or fractions).

Quick Tip: Always look for the largest square number that divides into your number - it'll save you time and effort!

$a surd is a square root which cannot be reduced to a rational number (integer or Haction). $ \sqrt{2}$ is a surd $ \sqrt{5}$ is a surd $ \s$

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Improve your grades

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Adding, Subtracting and Multiplying Surds

Adding and subtracting surds follows a simple rule: the surd parts must match! Think of it like collecting like terms in algebra. 4√3 + 5√3 = 9√3 because both terms have √3.

Remember: √a × √b = √(a × b) - this rule will be your best friend in surd calculations!