![surds and indices surds and indices](https://2.bp.blogspot.com/-g8XvjEbN8YM/WHxgInty_8I/AAAAAAAAEjQ/-Aj77nNxfEwi5YldFjlE-1JT2kp92byHgCLcB/s1600-rw/rsz_information_technology_act_2000-_explained.jpg)
a) Surds :
The surd is represented with symbol √ .The symbol √ is equals to ½.If we have a number and we are not able to obtain its root. It is called a surd.
The roots of those numbers which cannot be exactly obtained.
Like : √2,√3,√5,√6,√7 and so on.
Mixed Surds : A surd that /which we get by multiplying a surd and a rational number together are called mixed surd.
Like : 7√2,4√3,2√5,6√6,3√7
![](https://2.bp.blogspot.com/-Acutg_2Up0w/WHxY10vyDFI/AAAAAAAAEig/p3qNKRqPAFErvp4SmeZesZwydgD20i2UQCLcB/s640-rw/1.jpg)
we write x×x×x×x×x = xᶯ .here x is the base and n is the power of x.
![](https://3.bp.blogspot.com/-xQyZM_e8npA/WHxZJtARB3I/AAAAAAAAEik/VlrY6DtGWRwR_FH1LIHW4Eq92jFqhtlNQCLcB/s640-rw/2.jpg)
Properties of Surds
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Rules of addition for surds.
- Two similar surds can be added.
- Two dissimilar surds cannot be added.
b) Indices :
if ‘n’ is a positive integer and ‘a’ is a real number thenwe write x×x×x×x×x = xᶯ .here x is the base and n is the power of x.
![](https://3.bp.blogspot.com/-xQyZM_e8npA/WHxZJtARB3I/AAAAAAAAEik/VlrY6DtGWRwR_FH1LIHW4Eq92jFqhtlNQCLcB/s640-rw/2.jpg)