Question

find the square without actual multiplication=105​

Answer 1

Square of 105 is 11025.

Step-by-step explanation:

Here, we are told not to apply actual multiplication, that is we can not write get required square from direct product 105 × 105.

Method 1.

[ Using algebraic identity ]

We know that, (a + b)² = a² + 2ab + b²

Then, (105)²

= (100 + 5)²

= (100)² + 2 × 100 × 5 + (5)²

= 10000 + 1000 + 25

= 11025

Method 2.

[ Using distributive property ]

We know that, a × (b + c) = a × b + a × c

and (a + b) × c = a × c + b × c

Then, (105)²

= 105 × 105

= 105 × (100 + 5)

= 105 × 100 + 105 × 5

= 10500 + (100 + 5) × 5

= 10500 + 100 × 5 + 5 × 5

= 10500 + 500 + 25

= 11025

#SPJ3