Starter Remember the rules with Surds Any surd

Starter • Remember the rules with Surds. Any surd can be simplified by breaking it down as follows… Find 2 numbers that multiply to give this, one of which is square The square number can be simplified √ 27 √ 9 √ 3 3 √ 3 Find 2 numbers that multiply to give this, one of which is square The square number can be simplified √ 72 √ 4 √ 18 2 √ 9 √ 2 6 √ 2 But you can keep simplifying 2 lots of root 9 is equal to 6

Surd Sums • The rules with surds are exactly the same as the rules for algebra which you are familiar with… Algebra 3 x + 2 x = 5 x Surds 3√ 2 + 2√ 2 = 5√ 2 2 x - 4 y cannot be simplified 2√ 2 - 4√ 3 cannot be simplified a x b = ab √ 2 x √ 3 = √(2 x 3)

Surd Sums • Example Questions √ 5 + √ 45 √ 5 + √ 9√ 5 + 3√ 5 = 4√ 5

Surd Sums • Example Questions √ 28 - √ 7 √ 4√ 7 - √ 7 2√ 7 = √ 7

Surd Sums • Example Questions √ 18 + √ 72 √ 9√ 2 + √ 36√ 2 3√ 2 + = 9√ 2 6√ 2

Surd Sums • Example Questions √ 50 - √ 32 √ 25√ 2 - √ 16√ 2 5√ 2 = √ 2 4√ 2

Summary • We have recapped our knowledge of surds • We have seen that the rules are the same of those in algebra • We also know how to simplify sums involving different surds