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# Surds

/Tag: Surds
28 11, 2016

## Expanding Surds

By |2016-11-28T07:07:04+10:00November 28th, 2016||0 Comments

Expanding Surds worked examples Expand and simplify √3(10 - √2). = 10√3 - √6 multiply √3 by 10, remembering that if you multiply a number by a surd the number part stays out front of the surd, similar to 10 × y = 10y so 10 × √3 = 10√3 multiply √3 by √2, remembering [...]

28 11, 2016

## Dividing Surds

By |2016-11-28T07:04:44+10:00November 28th, 2016||0 Comments

Dividing Surds $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$ worked examples Simplify √10 ÷ √2. $\sqrt{10\div2}$ = √5 divide the surds part to form single surd and then simplify. Simplify 15√12 ÷ 3√6. = 5√2 think of this as two separate questions: divide the number parts by each other and then divide the surd parts [...]

28 11, 2016

## Multiplying Surds

By |2016-11-29T10:51:22+10:00November 28th, 2016||0 Comments

Multiplying Surds $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ $\sqrt{a}\times\sqrt{a}=a$ $\sqrt{a}^2=a$ worked examples Simplify √3 × √3.  = √9 = 3 multiply the things in the surds togetther as a single surd and then simplify. Simplify √3 × √5. $=\sqrt{3\times5}$ = √15 multiply the surds together and if they can't be simplified, then [...]

28 11, 2016

## Addding & Subtracting Surds

By |2017-01-12T15:36:50+10:00November 28th, 2016||0 Comments

Addding & Subtracting Surds worked examples Simplify 2√3 + √3.  = 3√3 Adding and subtracting surds works the same as algebra. they need to be like terms, so root 3 will be like with other root 3's. √3 is the same as saying 1√3 as x = 1x so [...]

7 05, 2016

## Rationalising The Denominator

By |2017-02-06T16:25:42+10:00May 7th, 2016||0 Comments

Rationalising The Denominator worked examples $\frac{1}{{\sqrt 2 }}$ When we have a single surd in the denominator then we multiply by that surd over itself to rationalise $=\frac{1}{{\sqrt 2 }} \times \frac{{\sqrt 2 }}{{\sqrt 2 }}$   $\frac{\sqrt 2 }{{2}}$     $\frac{7\sqrt3}{2\sqrt6}$ we only need [...]

7 05, 2016

## Single Surds

By |2017-02-19T11:20:29+10:00May 7th, 2016||0 Comments

Single Surds worked examples Express 2√2 as a single surd. = √4 × √2 this is the reverse process of simplifying a surd, so we look at what it was before it was simplified: the 2 was originally √4 and we can leave the √2 alone = 2√2 combine into [...]

7 05, 2016

## Expanding Binomial Surds

By |2016-11-28T06:05:29+10:00May 7th, 2016||0 Comments

Expanding Binomial Surds (a + b)2 = a2 + 2ab + b2 (a + b)2 = a2 + 2ab + b2 worked examples Expand and simplify (2 + √3)² = (2)2 + 2 x 2 x √2 + (√3)2 use the binomial expansion (a - b)2 = a2 - 2ab + [...]

7 05, 2016

## Simplifying Surds

By |2016-11-28T05:57:03+10:00May 7th, 2016||0 Comments

Simplifying Surds In order to simplify a surd, we need to break it down into it factors, at least one of which must be a perfect square. It is a good idea to consider a list of all the perfect squares. This has been dubbed The Good Factor List. [...]

7 05, 2016

## Surds

By |2016-11-28T07:05:39+10:00May 7th, 2016|Tags: , |0 Comments

Surds Go to the Surds Forum to see more questions or ask your own Topics Covered in Surds Simplifying Surds Adding and Subtracting Single Surds Multiplying Dividing Surds Expanding Surds Expanding Binomial Surds Rationalising The Denominator [...]

11 08, 2015

## Surd Problems

By |2017-03-20T20:20:57+10:00August 11th, 2015||0 Comments

Surd Problems worked examples Find the value of a and b such that (1 + √b)2 = a + √3. = (1)2 + 2 x 1 x √b + (√b)2 first expand the perfect square, it is easier to not deal with this as if it was an equation, just a [...]