Quantitative Aptitude · Mathematics

Squares and Square Roots

191 Questions

Squares and square roots questions assess numerical ability through perfect squares, digit properties, and fast calculation techniques. Many competitive exams feature Vedic mathematics shortcuts to solve these quickly. Mastering these rules improves overall calculation speed.

Perfect square propertiesVedic math squaresFinding square rootsDigit replacement puzzlesLeast perfect squares

Squares and Square Roots Questions

Multiple choice maths vedic mathematics square roots using vedic maths square and square roots using vedic mathematics history of mathematics

Find the square of the number $95$ using Vedic Mathematics.

  1. $9025$
  2. $9125$
  3. $8025$
  4. $8125$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
To find $(95)^{2}$
$100$ is the nearest power of $10$ which can be taken out as base.
Deviation is obtained by $95-100=-5$
Left side of the number is $95-5=90$
Since, the base is $100$, the right hand side number will have two digits and that can be obtained by taking square of deviation $-5$. So, $(-5)^{2}=25$.
Thus, the right side number will be $25$.
Hence, the required number is $9025$.
Multiple choice maths vedic mathematics square roots using vedic maths square and square roots using vedic mathematics history of mathematics

Find the square of the number $105$ using Vedic Mathematics.

  1. $11125$
  2. $11235$
  3. $11325$
  4. $11025$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
To find $(105)^{2}$
$100$ is the nearest power of $10$ which can be taken out as base.
Deviation is obtained by $105-100=5$
Left side of the number is $105+5=110$
Since, the base is $100$, the right hand side number will have two digits and that can be obtained by taking square of deviation $5$. So, $(5)^{2}=25$.
Thus, the right side number will be $25$.
Hence, the required number is $11025$.