Square roots shortcut

Trigonometry Tutorial

Square roots shortcut


There are times where you get a square root to simplify, but you have an option to use calculator. But wait, what if you don’t?
Well don’t worry, I can teach you to find an approximate value of square roots.

Sample Problem

Lets just take √10 and √97


For this method, you’ll need to find the closest perfect square.
for √10 , Square of 3 which is 9 is close.
Next, Subtract the perfect square from the original number without the roots, like this 10-9 = 1. Let this be called the difference of roots.
Now find the twice of the perfect number.Here it is 2 X 3 = 6.

Now to find the Square root, divide difference of roots by the twice of the perfect number. Here it is 1/6. Let us call this the decimal part.

Now to find the square root, take the perfect number is the whole number in mixed fraction. and the fractional part will be the decimal part.

By Solving mixed fraction, we get the approximate value of square root.
Value we found by this is 3.166..
Original value is 3.1622….

Well thats almost close.

Now for √97. closest perfect square is for 9, which is 81.
difference is 97-81 = 16
Value we found would be 9.88….
Original value is 9.84….

Good luck,
Shreyas Satheesh

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