Question

Multiply using "Urdhva Tiryagbhyam" Sutra.
$105\times 105$

Answer 1

$105\ast 105$

$\begin{array}{ccc}1& 0& 5\\ \ast 1& 0& 5\end{array}\_\_\_\_\_\_\_\_\_\_\_100050102\to carry\_\_\_\_\_\_\_\_\_\_11025\_\_\_\_\_\_\_\_\_\_$

$\to$ Multiply

the number in tens ( units) place $5\ast 5=25$ write $5$ in unit place and $2$ in tens place.

$\to$ Cross multiply tens and units place and add $0\times 5+0\times 5=0$ write $0$ in tens place and $0$ in hundred place carry

$\to$ Cross multiply hundreds and units place and add $1\times 5+1\times 5=10$

And multiply tens place and add it to $10$

$10+0=10$. write $0$ in hundreds place and $1$ in thousand place in carry.

$\to$ Cross multiply hundreds and tens place and add. $1\times 0+1\times 0=0$ write $0$ in thousand place and ${}^{\prime }{0}^{\prime }$ in tenthousand place in carry

$\to$ Now multiply hundreds place and write that number in tenthousand place $1\times 1=1$

$\to$ Now add and write the total

$105\ast 105=11025$.