8 1/ 2 Squared

by | June 05, 2016 | Math Made Easy! | No Comments

8mental math.

What is 8 1/2 x 8 1/2 ?

Traditional solution:

Convert to improper fractions:

8 ½ x 8 ½  = 17/2 x 17/2

Perform the multiplication:

17/2 x 17/2  = (17 x 17) /(2 x 2)

= 289/ 4

Convert to Mixed number: 72  1/ 4

MATH-Inic Mental solution:

This is an extension of the technique of squaring numbers ending in 5 where the answer is composed of two parts. The first part is obtained by using the Vedic Math Sutra “ By one more than the one before” and the second part is always 25.  For example 25 x 25 is 2 x (2+1)| 5 x 5 = 625.

Here the answer is simply 8 x (8 + 1)|1/2 x 1/ 2 = 72|1/4 = 72 1/4

Algebraic proof:

Use (a + b)2 = a2 + 2(a)(b) + b2

        (a + 1/2)2 = a2 + 2(a)(1/2) + (1/2)2

= a2 + a + (½)2

= a(a+1)+ ¼

For further explanations and more examples see MSC #15 Squaring numbers ending in 5, p 53, 25 Math Short Cuts

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