CBSE Class 11-science Answered

Take your base and power, a^b, and follow the steps below:

1. Take the log of the base a.
2. Multiply that number by the power. If the power is a root, you multiply the number by the fraction. For the square root, multiply the number by 1/2 or 0.5, for the cube root multiply by 1/3 or 0.333, and so on.
3. Do the opposite of what you did to compute the log by taking the number, and from your table or memory, find the number which would produce that product when taking the log. That is your answer.

Example 1
Suppose I want to find the square root of 36275. From the steps above...

1. Lets start by taking the log of 36725. We see that it is four decimal places to get to 3.6275 so the first number in the log is four. Using a log sheet or from our head.  We know that the log of 3.63 is about 0.56 and so the answer is 4.56.
2. Then multiply 4.56 by 1/2 (because We are taking the square root) which equals 2.28. On to the last step...
3. Now to find the number that when we take the log will be 2.28. Ignoring the integer 2 at the begining look at 0.28 and know that the log of 1.91 equals about 0.28. Then by moving the decimal to the right 2 times because that was the integer, We finally have our answer of 191. By checking with this with a calculator, we find that the estimation wasn't far off. The square root of 36725 is 191.6377... which is very close to 191.