Speed Maths Square Calculator (step-by-step solution)

Quick Start Guide

Speed Maths Square Calculator calculates square of a number using different speed maths methods. The methods are selected according to the number entered, to perform the calculations faster. It displays all the steps used for the calculations.

The methods used by this calculator are provided below.

1. Square of a number using Duplex Method or Dvandva Yoga (Vedic Mathematics)

Let's calculate $381^2$ using this method.

Step 1: Write the first row

The first row is obtained in the following pattern.

For a two digit number ab, first row is
D(a) | D(ab) | D(b)

For a three digit number abc, first row is
D(a) | D(ab) | D(abc)| D(bc)| D(c)

For a four digit number abcd, first row is
D(a) | D(ab) | D(abc)| D(abcd)| D(bcd)| D(cd)| D(d)

so on.

So, the first row for $381$ is
D($3$) | D($38$) |D($381$) | D($81$) |D($1$)

Note that D($3$) represents Duplex of $3,~$ D($38$) represents Duplex of $38$ and so on.

Step 2: Calculate Duplex

For a single digit number,
D(a)= a2

For a two digit number,
D(ab)= 2 × a × b

For a three digit number,
D(abc)= 2 × a × c + b2

For a four digit number,
D(abcd)= 2 × a × d + 2 × b × c

For a five digit number,
D(abcde)= 2 × a × e + 2 × b × d + c2

Thus, for our example
D($3$) $=3^2=9$
D($38$) $=2×3×8=48$
D($381$) $=2×3×1+8^2=70$
D($81$) $=2×8×1=16$
D($1$) $=1^2=1$

Write it in the order
$9~~|~~48~~|~~70~~|~~16~~|~~1$

Step 3: Adjust Carries as applicable.

Take our example. From $16,$ take $1$ as carry which is added to $70$ making it $71$

Thus we have
$9~~|~~48~~|~~71~~|~~6~~|~~1$

Repeat this process from right to left. So, from $71$, take $7$ as carry which is added to $48$ making it $55$

Thus we have
$9~~|~~55~~|~~1~~|~~6~~|~~1$

From $55$, take $5$ as carry which is added to $9$ making it $14$

Thus we have
$14~~|~~5~~|~~1~~|~~6~~|~~1$

Combining these groups, we get the answer as
$145161$

2. Square of a number close to $50$
3. Square of a number close to powers or $10$
4. Square of a number close to multiples of powers of $10$
5. Square of a number close to multiples of powers of $10$
6. Equidistant Method
7. Square of numbers using $(a+b)^2=a^2+2ab+b^2$
8. Square of numbers using $(a-b)^2=a^2-2ab+b^2$

Calculate squares of different numbers using this calculator and get familiar with these speed maths methods for squares. Once we have a fair understanding of these, squares can be calculated faster, which is obviously an advantage in competitive examinations.

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