Question 14

What is the simplified value of $$\sqrt{\frac{(0.07)^2+(0.29)^2-0.0203}{(0.07)^3+(0.29)^3}}$$

Solution

Expression : $$\sqrt{\frac{(0.07)^2+(0.29)^2-0.0203}{(0.07)^3+(0.29)^3}}$$

Let $$0.07=x$$ and $$0.29=y$$

= $$\sqrt{\frac{(x)^2+(y)^2-(xy)}{(x)^3+(y)^3}}$$

Using, $$(x^3+y^3)=(x+y)(x^2+y^2-xy)$$

= $$\sqrt{\frac{(x^2+y^2-xy)}{(x+y)(x^2+y^2-xy)}}$$

= $$\sqrt{\frac{1}{x+y}}=\sqrt{\frac{1}{0.07+0.29}}$$

= $$\frac{1}{0.36}=\frac{1}{0.6}$$

=> Ans - (C)

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