Squares using vedic method or quicker calculation

Dwandh Yog Method
 Find the squares of following: -
1. 𝟐𝟕 𝟐
2. 𝟖𝟑 𝟐
3. 𝟏𝟏𝟕 𝟐
4. 𝟐𝟓𝟓 𝟐

Here are few steps to solve the given squares in few steps as:
 For two digit numbers say (xy) we break it as
 Square of first digit in left side, forwards slash
 Twice of the given number, slash
 Square of last digit in right side, it is written as
𝒙 𝟐
/(𝟐 × 𝒙 × 𝒚)/𝒚 𝟐
 Let us understand by an example as:

 𝟐𝟕 𝟐
Let us break the given as
𝒙 𝟐/𝟐 × 𝒙 × 𝒚/𝒚 𝟐
 𝟐 𝟐/𝟐 × 𝟐 × 𝟕/𝟕 𝟐
4/28/49
4/2(8+4)/9
4/2(12)/9
4/(2+1)/2/9
(4+3)/2/9
7/2/9, now write from right hand side as,
729

 𝟖𝟑 𝟐
𝒙 𝟐/𝟐 × 𝒙 × 𝒚/𝒚 𝟐
 𝟖 𝟐/𝟐 × 𝟖 × 𝟑/𝟑 𝟐
64/48/9
Now we can write above in the form as from right hand side
4/(4+4)/8/9
4/8/8/9
4889 ans.

Here are few steps to solve the given squares in few steps as:
 For 3 digit numbers say xyz we break it as [(x) & (yz)]
 Square of first digit in left side, forwards slash
 Twice of the given number, slash
 Square of last digit in right side, it is written as
𝒙 𝟐
/𝟐 × 𝒙 × (𝒚𝒛)/(𝒚𝒛) 𝟐
 Let us understand by an example as:

 𝟏𝟏𝟕 𝟐
𝒙 𝟐
/𝟐 × 𝒙 × (𝒚𝒛)/(𝒚𝒛) 𝟐
 𝟏 𝟐/𝟐 × 𝟏 × 𝟏𝟕/𝟏𝟕 𝟐
1/34/289
1/34+2/89
1/36/89
13689

 𝟐𝟓𝟓 𝟐
𝒙 𝟐/𝟐 × 𝒙 × (𝒚𝒛)/(𝒚𝒛) 𝟐
 𝟐 𝟐/𝟐 × 𝟐 × 𝟓𝟓/𝟓𝟓 𝟐
4/220/3025
4/2/20+30/25
4/2/50/25
4+2/50/25
6/50/25
65025

Conclusion
• Hence we conclude that for squaring any numbers we use the formula for:
• 𝑎2 + 2 × 𝑎 × 𝑏 + 𝑏2,
• a = first digit from left & b = last digit from right side
• For 3 digit take a = first digit from left & b = last 2 digit
• For 4 digit take a = first 2 digit from left & b = last 2 digit
• For 5 digit take a = first 2 digit from left & b = last 3 digit and so on.

Squares using vedic method or quicker calculation

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