Question

find the square of 45 without doing actual multiplication?

Answer 1

$4(4 + 1).5 \times 5 \\ 4 \times 5.25 \\ 2025$

Answer 2

(45)^2

(40 + 5) ^2

Using identity,
(a + b) ^2 = a^2 + 2ab + b^2

(40 + 5)^2 = 40^2 + 2 × 40 × 5 × 5^2

(40 + 5)^2 = 1600 + 400 + 25

(40 + 5)^2 = 2025

Ans. 45^2 = 2025

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