N8: calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares (e.g. √12 = √(4 × 3) = √4 × √3 = 2√3) and rationalise denominators

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What is a surd?

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13 Terms

1

What is a surd?

Surds are the square roots (√) of numbers that cannot be simplified into a whole or rational number, also called irrational numbers

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2

Is √4 a surd?

No because it can be simplified into ±2 - surds cannot be simplified into whole numbers

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3

What is good about a surd?

Surds are the exact value - if it was converted into a regular number, it wouldn’t be exact

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4

What is rationalising?

Removing any surds from the denominator of a fraction

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5

How to rationalise

If the denominator contains only a surd, multiply the whole fraction by that surd

If the denominator contains a surd and another number added or subtracted from it, multiply the fraction by that surd, number but with the opposite symbol (+ would become - and vice versa)

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6

Rationalise (5-√3)/√2

Multiply the numerator by the surd (√2): (5-√3)√2=5√2-√6

Multiply the denominator by the surd (√2): √2²=2

Write the answer: (5√2-√6)/2

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7

Rationalise √7/2+√7

2√7-7/-3

<p>2<span>√7-7/-3</span></p>
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8

What is calculating with pi?

Similarly to a surd, pi represents an exact number with thousands of decimal places - in order to keep its exact value, we use the symbol 𝜋

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9

How to calculate with 𝜋

When answering a question, keep the result in terms of 𝜋, such as 12𝜋 cm

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10

Calculate the area of a circle with a radius of 3, leaving the answer in terms of 𝜋

Area of a circle = 𝜋r²

𝜋x3²=9𝜋

Answer=9𝜋 cm² (this is a more exact answer than 28.27)

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11

How to simplify surds

1) Split the surd into a square number multiplied by another number

2) square root the number and take it outside of the square root

3) leave the other number unless it can be simplified further

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12

Simplify √50

√50=√25x√2

√25=5

5√2

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13

Simplfy 6√60

√60=√4x√15

2√15×6=12√15

12√15

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