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Today, the topic which we are going to discuss is the 'General Procedure to Square any number'. Earlier we discussed about the squaring of numbers near base, however, general procedure is another nice formula to do the squaring and is applicable universally. The method or sutra is "Vertically and Crosswise", but here it is used in a different sense; based on a procedure known as 'Dwandwa Yoga' or 'Duplex Combination Process' or 'Duplex'; denoted as (D).
'Duplex' term is used in two different sense; for squaring and for multiplication. And for current formula, it will be used in both the senses. If we are having a single or central digit, then 'Duplex' means squaring that digit (a2 ). Secondly it can be used for even digits number or on numbers having equidistant digits, then 'Duplex' means to double of cross multiplication of the equidistant numbers (2ab). This concept is very important to understand the current formula and will be used in future articles also. Let us see few example to understand it more:
For 1 digit – D(a) = single digit = a2
e.g. D(5) = 52 = 25
For 2 digits – D(ab) = even digits number = twice the product of the digits (2ab)
e.g. D(26) = 2(2)(6) = 24
For 3 digits – D(abc) = product of equidistant digits from center and square of center digits
= twice the product of the outer digits (2ac) + the square of the middle digit (b2 )
e.g. D(734) = 2(7)(4) + 32
= 56 + 9 = 65
For 4 digits – D(abcd) = product of equidistant numbers
= twice the product of the outer digits (2ad) + twice the product of the inner digits (2bc)
e.g. D(1034) = 2(1)(4) + 2(0)(3)
= 8 + 0 = 8
For 5 digits – e.g. D(10345) = product of equidistant digits and square of center digits
= 2(1)(5) + 2(0)(4) + 32
= 10 + 0 + 9 = 19
and so on. This is called Duplex.
Today, the topic which we are going to discuss is the 'General Procedure to Square any number'. Earlier we discussed about the squaring of numbers near base, however, general procedure is another nice formula to do the squaring and is applicable universally. The method or sutra is "Vertically and Crosswise", but here it is used in a different sense; based on a procedure known as 'Dwandwa Yoga' or 'Duplex Combination Process' or 'Duplex'; denoted as (D).
'Duplex' term is used in two different sense; for squaring and for multiplication. And for current formula, it will be used in both the senses. If we are having a single or central digit, then 'Duplex' means squaring that digit (a2 ). Secondly it can be used for even digits number or on numbers having equidistant digits, then 'Duplex' means to double of cross multiplication of the equidistant numbers (2ab). This concept is very important to understand the current formula and will be used in future articles also. Let us see few example to understand it more:
For 1 digit – D(a) = single digit = a2
e.g. D(5) = 52 = 25
For 2 digits – D(ab) = even digits number = twice the product of the digits (2ab)
e.g. D(26) = 2(2)(6) = 24
For 3 digits – D(abc) = product of equidistant digits from center and square of center digits
= twice the product of the outer digits (2ac) + the square of the middle digit (b2 )
e.g. D(734) = 2(7)(4) + 32
= 56 + 9 = 65
For 4 digits – D(abcd) = product of equidistant numbers
= twice the product of the outer digits (2ad) + twice the product of the inner digits (2bc)
e.g. D(1034) = 2(1)(4) + 2(0)(3)
= 8 + 0 = 8
For 5 digits – e.g. D(10345) = product of equidistant digits and square of center digits
= 2(1)(5) + 2(0)(4) + 32
= 10 + 0 + 9 = 19
and so on. This is called Duplex.
