Question

Using identities, evaluate:
$1.05\times 9.5$

• A. $9.975$
• B. $0.9975$
• C. $99.75$
• D. $0.09975$

Answer 1

The correct option is A $9.975$

$1.05\times 9.5=1.05\times 0.95\times 10$
$=(1+0.05)(1-0.05)\times 10$
$=\left[\right(1{)}^2-\left(0.05{)}^2\right]\times 10$
$=[1-0.0025]\times 10$
$\left[Usingidentity\right(a-b\left)\right(a+b)=a^2-b^2]$
$=0.9975\times 10$
$=9.975$