Find the value of each of the following, using the column method:
$$(23)^{2}$$
Given number $$=23$$
By using column method we have,
$$\therefore a=2$$ and $$b=3$$
Steps involved in solving column method:
Step $$1$$: Make three columns headed by $$a^{2}, 2\times a\times b$$ and $$b^{2}$$ respectively. Write the values of $$a^{2}, 2\times a\times b$$ and $$b^{2}$$ in columns respectively.
Step $$2$$: In third column underline the unit digits of $$b^{2}$$ i.e $$9$$ and carry the tens digit of it i.e. $$0$$ to the second column and add it to the value of second column is $$2\times a\times b$$ and it will remains $$12$$ if it added to $$0$$.
Step $$3$$: In column second, underline the unit digit of the number obtained in second step i.e. $$2$$ and carry over the ten digit of it to first column and add it to the value of $$a^{2}$$ i.e. $$4+1=5$$
Step $$4$$: Now underline the number obtained in third step in first column i.e. $$5$$. The underlined digits give the required square number.
| $$a^2$$ | $$2ab$$ | $$b^2$$ |
$$2^2 =4\\ +1$$
$$5$$ | $$2\times 2\times 3 =\underline{1}2\\ +0$$
$$2$$ | $$3^2=\underline{0}9$$
$$9$$ |
$$\therefore (23)^{2}=529$$