Respuesta :
well if you're referring to rationalizing [tex]\bf \cfrac{2}{\sqrt{2}}[/tex], which simply means, getting rid of the pesky radical at the bottom
well, it boils down to, hmm say... a quantity or even a polynomial, multiplied times 1, is itself, 2*1=2, 3*1 = 3, ducks*1 = ducks, spaghetti * 1 = spaghetti
or whatever * 1 = whatever
and the value of the multiplicand, doesn't change in anyway, is the same thing before and after the multiplication by 1
now....1 can also be a fraction [tex]\bf \cfrac{2}{2}=1\qquad \cfrac{3}{3}=1\qquad \cfrac{1,000,000}{1,000,000}=1 \\\\\\ \cfrac{ducks}{ducks}=1\qquad \cfrac{spaghetti}{spaghetti}=1\qquad \cfrac{cheese}{cheese}=1 \\\\\\ \cfrac{\textit{the quick fox jumped}}{\textit{the quick fox jumped}}=1\qquad \cfrac{whatever}{whatever}=1[/tex]
so.. when you're doing [tex]\bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\iff \cfrac{2}{\sqrt{2}}\cdot1[/tex]
and the value multiplicand doesn't change in any way
now, try this in your calculator [tex]\bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{\sqrt{2^2}}\implies \cfrac{2\sqrt{2}}{2}\implies \sqrt{2}\\\\ -----------------------------\\\\ \textit{check how much is }\cfrac{2}{\sqrt{2}}\textit{ in your calculator} \\\\\\ \textit{then check how much is }\sqrt{2}\textit{ in it}[/tex]
well, it boils down to, hmm say... a quantity or even a polynomial, multiplied times 1, is itself, 2*1=2, 3*1 = 3, ducks*1 = ducks, spaghetti * 1 = spaghetti
or whatever * 1 = whatever
and the value of the multiplicand, doesn't change in anyway, is the same thing before and after the multiplication by 1
now....1 can also be a fraction [tex]\bf \cfrac{2}{2}=1\qquad \cfrac{3}{3}=1\qquad \cfrac{1,000,000}{1,000,000}=1 \\\\\\ \cfrac{ducks}{ducks}=1\qquad \cfrac{spaghetti}{spaghetti}=1\qquad \cfrac{cheese}{cheese}=1 \\\\\\ \cfrac{\textit{the quick fox jumped}}{\textit{the quick fox jumped}}=1\qquad \cfrac{whatever}{whatever}=1[/tex]
so.. when you're doing [tex]\bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\iff \cfrac{2}{\sqrt{2}}\cdot1[/tex]
and the value multiplicand doesn't change in any way
now, try this in your calculator [tex]\bf \cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{2\sqrt{2}}{\sqrt{2^2}}\implies \cfrac{2\sqrt{2}}{2}\implies \sqrt{2}\\\\ -----------------------------\\\\ \textit{check how much is }\cfrac{2}{\sqrt{2}}\textit{ in your calculator} \\\\\\ \textit{then check how much is }\sqrt{2}\textit{ in it}[/tex]
