Starter 1 Simplify the following without a calculator

Starter 1) Simplify the following without a calculator a) 2) b) What does it mean to ‘simplify’ something in the above way? To write something equivalent, using smaller integer values

Surds • Any number that can be written as either an integer or a fraction is said to be rational • Eg) 2 is rational 0. 5 is rational ( 1/ 2 ) 3. 62 is rational (3 62/100 = 362/ 100)

Surds • Some numbers cannot be written as a fraction. As a decimal, they go on forever following a non-repeating pattern • π is irrational • So is √ 2 • So is √ 5 (3. 1412……. . ) (1. 412………) (2. 236………)

Surds • To avoid rounding errors, we can leave some answers in ‘surd form’ • This means we do not simplify to 2 dp etc • Eg) x² - 4 = 6 x² = 10 (+4 to both sides) x = √ 10

Surds • We can simplify some surds…. √ 20 √ 4 x √ 5 2√ 5 (As 4 x 5 is 20)

Surds • We can simplify some surds…. √ 18 √ 9 x √ 2 3√ 2 (As 9 x 2 is 18)

Surds • Be careful… 3√ 5 is different to 3√ 5 This means ‘ 3 times the square root of 5’ This means ‘the cube root of 5’

Surds • Write the following as a whole number: √ 3 x √ 12 √ 36 6

Surds • Write the following as a whole number: √ 32 x √ 2 √ 64 8

Surds • Write the following as a whole number: √ 20 ÷ √ 5 √ 4 2

Surds • This process only works where all parts are Surds… √ 50 x √ 2 = 10 If both terms are Surds, they can be put together under the root sign… = 50√ 2 If one isn’t, simplify like in Algebra… = √ 100 eg) 50 x a = 50 a

Summary • We have learnt what Surds are, and why they are used • We have seen how to ‘break up’ a Surd into 2 parts • We have also looked at putting a Surd ‘back together’