Evaluate 49 square minus 47 square without actually calculating the squares

Question

asked Jun 15, 2024 148k views

1 Answer

Ralf H · Answer 1 · 2024-06-22T01:58:49+0000

Hello!

Answer:

$\Large \boxed{\sf 192}$

Explanation:

→ We want to calculate 49² - 47² without actually calculating the squares.

→ We know:

$\sf a^2 - b^2 = (a + b)(a - b)$

→ In our expression:

$\sf a = 49\\b = 47$

→ So:

$\sf 49^2 - 47^2 = (49 + 47)(49 - 47)$

→ Let's simplify the expression:

$\sf (49 + 47)(49 - 47)\\\\ = 96 * 2\\\\\boxed{\sf= 192}$

Conclusion:

49² - 47² is equal to 192.