Question

Find the squares of the following numbers without actual multiplication.
(i) 65
(ii) 95
(iii) 205​

Answer 1

Answer:

simple ok so for 65 it is 4225 95 it is 9025 and 205 it is 42025For example 65 first take the digit at hundreds place and multiply it by its consecutive number here 7 so 7x6 =42 and now for the units place 5 which is common in this trick write it's square 25 now mix these two digits for the ans 4225! plz make brainliest

Answer 2

Step-by-step explanation:

$i) \: \: \: \: {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ {(65)}^{2} = {(100 - 35)}^{2} \\ = {(100)}^{2} + {(35)}^{2} - 2 \times 100 \times 35 \\ = 10000 + 1225 - 7000 \\ = 4225$

$ii) \: \: \: \: {(95)}^{2} = {(100 - 5)}^{2} \\ = {(100)}^{2} + {(5)}^{2} - 2 \times 100 \times 5 \\ = 10000 + 25 - 1000 \\ = 10025 - 1000 \\ = 9025$

$iii) \: \: \: \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ {(205)}^{2} = {(200 + 5)}^{2} \\ = {(200)}^{2} + {(5)}^{2} + 2 \times 200 \times 5 \\ = 40000 + 25 + 2000 \\ = 40025 + 2000 \\ = 42025$

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