Surds
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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 Laws of indices, 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.
Chapter 4: Indices, standard form and surds
- Laws of indices 5 min
- Standard form 5 min
- Surds 5 min
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