Question 9

The square root of$$ \frac{(0.75)^{3}}{1-0.75}+[0.75+(0.75)^{2}+1]$$

Solution

let us consider 0.75 as x. then equation becomes

$$ \sqrt[2]{x^3/(1-x) +(x+x^2+1)}$$

= $$ \sqrt[2]{[x^3 +(1-x)(x+x^2+1)] \div (1-x)}$$

= $$ \sqrt[2]{[x^3 +(1-x^3)] \div (1-x)}$$

= $$ \sqrt[2]{1 \div (1-x)}$$

If x is replaced by 0.75, we get

= $$ \sqrt[2]{1 \div 0.25}$$

= $$ \sqrt[2]4$$

=2

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