Question 9 of 43intermediate🔧 ApplyNumerical6 marks

Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier.

(i)

1172117^{2}

Answer

13689

(ii)

78278^{2}

Answer

6084

(iii)

1982198^{2}

Answer

39204

(iv)

2142214^{2}

Answer

45796

(v)

110421104^{2}

Answer

1218816

(vi)

112021120^{2}

Answer

1254400

Explanation

To make calculations easier, we express the given numbers as the sum or difference of numbers ending with zeros (like multiples of 10, 100, or 1000). This allows us to easily apply the identities (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2. For numbers slightly less than a round number, (a−b)2(a-b)^2 is most convenient, while for numbers slightly more, (a+b)2(a+b)^2 is preferred.

PreviousNext