Surds
Watch the whole lecture free
Make a free account to watch every lecture to the end: 8 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
That was the teaching part. The rest of this lecture is free with an account: 8 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
The teaching part (1 min) is free to watch. A free account opens the whole lecture: 8 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- The exact diagonal
- What is a surd?
- The product rule
Read the transcript of the teaching part
Last time
Before we start: last time, in Standard form, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The exact diagonal
A square tile has side one. Its diagonal is the square root of two: one point four one four two one three five six, and the digits never stop. A calculator gives only an approximation. A surd keeps the answer exact. Today you simplify surds, calculate with them, and remove them from the bottom of a fraction.
What is a surd?
A surd is a root that cannot be simplified to a whole number or a fraction. The square root of two, and the square root of seven are surds. Their decimals never end. The square root of nine is three, so it is not a surd.
The product rule
The root of a product is the product of the roots. Use it to split a surd into a square number and a remainder. To simplify the square root of seventy-two, find the biggest square factor. Thirty-six times two is seventy-two. So the root is root thirty-six times root two, which is six root two.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Surds.
The whole chapter: Indices, Standard Form and Surds.
Chapter 4: Indices, standard form and surds
- Laws of indices 5 min
- Standard form 6 min
- Surds 5 min
Also for IGCSE Maths 0580
Which topics come up most in IGCSE Maths 0580 past papers, counted from every paper since 2004.