Multiplication Tricks (4)

Algebra Level 2

Find the value of

35 2 \large { 35 }^{ 2 }

Try without the use of a calculator

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The answer is 1225.

Angela Fajardo by Angela Fajardo , 19, Philippines

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4 solutions

Ashish Menon
Dec 25, 2016

35 = 50 − 15 35 = 50 - 15 .
So 3 5 2 = ( ( 25 − 15 ) ‾ ( 15 ) 2 ‾ = 1225 35^2 = (\overline{(25 - 15)}\overline{{(15)}^2} = 1225 . Note that 15 2 {15}^2 has three digits but we can only filk up two digits in the end, so the hundredth digit 2 is carried on and added to the second number of the answer.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Zee Ell
Nov 2, 2016

3 5 2 = ( 30 + 5 ) 2 = 3 0 2 + 2 × 5 × 30 + 5 2 = 900 + 300 + 25 = 1225 35^2 = (30+5)^2 = 30^2 + 2×5×30 + 5^2 = 900 + 300 + 25 = \boxed {1225}

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Viki Zeta
Nov 2, 2016

( 10 a + 5 ) 2 = 100 a 2 + 100 a + 25 = 100 a ( a + 1 ) 25 = a ( a + 1 ) ‾ 25 ‾ (10a + 5)^2 = 100a^2 + 100a + 25 = 100a(a+1) 25 = \overline{a(a+1)}\overline{25}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Razzi Masroor
Nov 16, 2016

(35)^2=(7x5)^2=49x25=50x25-25=1225

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