Question

Find the value of each of the following using the short-cut method:
1.$(25{)}^3$ 2. $(47{)}^3$ 3. $(68{)}^3$ 4. $(84{)}^3$

Answer 1

1. $(25{)}^3$ = We know that short-cut method for finding the cube of any two digit number is as given.
$(a+b{)}^3=a^3+3a^{2}b+3a{b}^2+b^3$
= $a^2\times a+a^2\times 3b+b^2\times 3a+b^2\times b$
Here a=2, b=5

$\therefore (25{)}^3=15625$
2. $(47{)}^3$= Here a=4, b=7

$\therefore (47{)}^3$= 103823
3. $(68{)}^3$ = Here a = 6, b=8

$\therefore (68{)}^3=314432$
4. $(84{)}^3$ = Here a = 8, b=4

$\therefore (84{)}^3=592704$