Question 190

Find the square root of $$\frac{(0.064-0.008)(0.16-0.04)}{(0.16+0.08+0.04)(0.4+0.2)^3}$$

Solution

we need to find the value of $$\sqrt{\frac{(0.064-0.008)(0.16-0.04)}{(0.16+0.08+0.04)(0.4+0.2)^3}}$$

= $$\sqrt{\frac{(0.4^3-0.2^3)(0.4^2-0.2^2)}{(0.16+0.08+0.04)(0.4+0.2)^3}}$$

= $$\sqrt{\frac{(0.4-0.2)(0.4^2+0.2^2+0.4\times 0.2)(0.4-0.2)(0.4+0.2)}{(0.16+0.08+0.04)(0.4+0.2)^3}}$$

= $$\sqrt{\frac{(0.4-0.2)^2}{(0.4+0.2)^2}}$$

= $$\sqrt{\frac{1}{9}}$$

= $$\frac{1}{3}$$

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