Question

If 6.4² = 40.96, write the values of the following:

(1) 64²
(2) (0.064)²
(3) 0.64²

Answer 1

It is given that 6.4² = 40.96

(1) (64)²
= (64 × 64)
= (6.4 × 10 × 6.4 × 10)
= (6.4)² × (10)²
= 40.96 × 100
= 4096

(2) (0.064)²
$$\begin{gathered} ={\left(\frac{64}{1000}\right)}^2 \\ ={\left(\frac{6.4}{100}\right)}^2 \\ =\frac{{\left(6.4\right)}^2}{{\left(100\right)}^2} \\ =\frac{40.96}{10000} \\ =0.004096 \end{gathered}$$

(3) 0.64²
$$\begin{gathered} ={\left(\frac{64}{100}\right)}^2 \\ ={\left(\frac{6.4}{10}\right)}^2 \\ =\frac{{\left(6.4\right)}^2}{{\left(10\right)}^2} \\ =\frac{40.96}{100} \\ =0.4096 \end{gathered}$$