Question

I need someone to tell me what to do in these, i have no clue how to get it.

Answer 1

To convert a decimal to a fraction, we simply "add as many zeros to the denominator as there are decimals, and lose the dot", what the dickens does that mean?

well, let's see, notice in this case, the radicand has 4 decimals, so we'll use 4 zeros to make it a fraction, and lose the dot,

$\bf \pm\sqrt{0.0081}\\\\ -------------------------------\\\\ 0.\underline{0081}\implies \cfrac{00081}{1\underline{0000}}\implies \cfrac{81}{10000}\implies \cfrac{9^2}{100^2}\\\\ -------------------------------\\\\ \pm\sqrt{\cfrac{9^2}{100^2}}\implies \pm\cfrac{\sqrt{9^2}}{\sqrt{100^2}}\implies \pm\cfrac{9}{100}$



as for the other one

$\bf 5x^2-21=39\implies 5x^2=60\implies x^2=\cfrac{60}{5}\implies x^2=12 \\\\\\ x=\pm\sqrt{12}\implies x=\pm\sqrt{4\cdot 3}\implies x=\pm\sqrt{2^2\cdot 3}\implies x=\pm 2\sqrt{3}$