Question

Using suitable identities find (1092)^2.

Answer 1

Answer:

$1092 ^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = {(1100 - 8)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 1100 ^{2} - 2 \times 1100 \times 8 + 8 ^{2} \\ = 1210000 - 17600 + 64 \: \: \: \: \: \: \: \: \\ = 1192464 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

HOPE THIS WILL HELP YOU

Answer 2

Given:

A number in the exponential form (1092)².

To Find:

The expansion of the above form using suitable identities.

Solution:

1. Consider the given number (1092)².

2. The given number can be also written as,

=> (1092)² = (1000+92)²,

3. The formula for the expansion of (a+b)² is,

=> (a+b)² = a² + b² + 2ab,

4. Use the above formula to find the value,

=> (1000+92)² = 1000² + 92² + 2 x 1000 x 92,

=> (1000+92)² = 1000000 + 8464 + 184000,

=> (1000+92)² = 1192464.

Therefore, the value of (1092)² is 1192464.