Try to evaluate the following using a suitable identity: Class 9

Try to evaluate the following using a suitable identity: Class 9

Question 1.

Try to evaluate the following using a suitable identity: Class 9

i. 35²

ii. 65²

iii. 85²

iv. 105²

Do you observe any interesting pattern?

Answer:

Using identity: a² = (a + b)(a - b) + b²

i. 35² = (35 + 5)(35 - 5) + 5² = 40 × 30 + 25

= 1200 + 25 = 1225

ii. 65² = (65 + 5)(65 - 5) + 5² = 70 × 60 + 25

= 4200 + 25 = 4225

iii. 85² = (85 + 5)(85 - 5) + 5² = 90 × 80 + 25

= 7200 + 25 = 7225

iv. 105² = (105 + 5)(105 - 5) + 5² = 110 × 100 + 25

= 11000 + 25 = 11025

Pattern observed:

For any number ending in 5, its square always ends in 25. The digits before 25 are obtained by multiplying the number formed by the remaining digits by its next consecutive number.

For example,

65²: 6 × 7 = 42

So, 65² = 4225