![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyKLR4y7hzetkcxlCH9yRaA0zppzfp9P-RxTisYx474ZUX0x3WxLsvRIsArN8-IpCVt1IJko7lmolh59EldvJ1n44iFkoXKuhuMxvw7264AqSALxS9oGoKj51cQayXJggjV1yMmmeEMWjS/s400/200662918393174770.jpg)
Expressions with Indices, surds, exponentials and powers are the inverse of logarithm.
Indices and surds has real and known number.
Exponentials has unknowns, for example "X".
Logarithm of a number means the "exponential" of the base.
The flying pair of cranes is from http://www.cpedu.org/bbs/attachments/dvbbs/2006-6/200662918393174770.jpg
Normally in indices we come across square root of numbers giving results which are evaluated as exact number, just like the following.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb3fyOejEAihlnr6_6lnH-LdZrP3d6UJxEOHWbKQP5ld-xoVsuNaunlz1oESU1TtoV1FrunXjxk8KtWXERYGty4exTuj9mexvsTHmgzNXbPCZCCJA23nY2Adlq-9V5Z_D8_jHLr9lm25z3/s400/Rational+roots.jpg)
However there are also square root of numbers that do not evaluate exactly. The examples below shows some of those irrational results also called irrational roots.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwiBdOUdSOzUUWCwhEmXRwr-NP-niwkIknHyUnfFcPDyCqR6hwlzqdPKvlk5VOMBR74L4BslMkW3cudTCmz1jKmZMLywmPUxoIkV6OzPr_yKGNMzKRMGLgznujd9jTz8QNpSzjKQZtp6tI/s400/Irrational+roots.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_WhjrLyqv7vychzc2V8e8M_EysFAxn5lBlh9LAj93xEBFnoRIR4mwDZQv0e9gf2XdZ7nkZdwaRGx4tCYp6Nn-xrIo2QOAaxNq794ZaxoHqYbXPg7v83HWA9Aa8F5Ph5pIt937bnoLYLxl/s400/Roots+not+evaluated+exactly+are+irrational+roots.jpg)
Numerical expressions which contain irrational roots are called surds.
Examples of surds. Conjugate surds exist too. They are a similar pair of expressions but one is with a negative and the other is with a positive irrational part.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfWkVcK2fePUAt5JegHFBiCXUpM5kSswWPOlsqQy5O5Zot-jYWbDhSH1tqwXZxvp1tZM_XX78S04Mx2UvdSD-_A8yMTv7D6y7eQmw5eXNyrg9qc5idXf7u885wHdB2MfhtTdo18DPNIknj/s400/Numerical+expressions+which+contain+irrational+roots+are+called+surds.jpg)
Reference
http://www.heymath.com/heymath/ (requires login ID and password)
http://www.mathsteacher.com.au/year9/ch07_surds/03_surds/surds.htm
http://www.cpedu.org/bbs/attachments/dvbbs/2006-6/200662918393174770.jpg