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

About The Author

Love To Teach KIDS..
I am currently in high school. I wish to help kids of lower grades in Math and Science. I do well at Math and Science. I can help students till 8th Grade as I think my knowledge is enough for them. Personally, I like experimenting stuff everyday.
8 Subjects
KnowRo Tutor
2 Tutorials
Chennai, TN
Get Tutoring Info

Suggested Tutors for Trigonometry Help

Greg S

Dover, NH

Your Math Tutor

Altai P

Durham, NH

Science And Math Tutor

Laurice H

Hampton, NH

High School Mathematics And SAT Tutor

Paul P

Dover, NH

Math Subject Matter Expert And SAT Instructor