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  4. The square root of (0.081/0.0064) × (0.484/6.25) × (25/121)

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Q. The square root of $\frac{0.081}{0.0064} \times \frac{0.484}{6.25} \times \frac{25}{121}$

Squares and Square Roots and Cubes and Cube Roots

Solution:

$\left(\frac{0.081}{0.0064} \times \frac{0.484}{6.25} \times \frac{25}{121}\right)^{\frac{1}{2}}$
$=\left(\frac{81 \times 10^{-3}}{64 \times 10^{-4}} \times \frac{484 \times 10^{-3}}{625 \times 10^{-2}} \times \frac{25}{121}\right)^{\frac{1}{2}} $
$=\left(\frac{81 \times 484 \times 25 \times 10^{-3-3}}{64 \times 625 \times 121 \times 10^{-4-2}}\right)^{\frac{1}{2}}$
$ =\left(\frac{81 \times 484 \times 25}{64 \times 625 \times 121}\right)^{\frac{1}{2}} $
$ =\frac{(81)^{\frac{1}{2}} \times(484)^{\frac{1}{2}} \times(25)^{\frac{1}{2}}}{(64)^{\frac{1}{2}} \times(625)^{\frac{1}{2}} \times(121)^{\frac{1}{2}}}=\frac{9 \times 22 \times 5}{8 \times 25 \times 11} $
$=\frac{9}{20} $
$ =0.45$