sqrt(2)/sqrt(2) = 1 ... you can multiply any number by 1 without changing the value, so this method is often used to simplify complex fractions like 1 / sqrt(2)
You have to rationalize the denominator, so 1/sqrt(2) would be multiplied by sqrt(2)/sqrt(2), leaving you with (1*sqrt(2))/(sqrt(2)*sqrt(2)), or sqrt(2)/sqrt(2)^2. In other words, you'd be left with sqrt(2)/2.
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1 / √2
= (1 / √2) (√2 / √2) --- {Since √2 / √2 = 1, I am multiplying by 1 and not changing the value}
= √2 / √2√2
= √2 / 2
Multiply the value by 1. Yep, that's how without changing the value as 1 times anything = anything.
In this case 1 = sqrt(2)/sqrt(2) so 1 * 1/sqrt(2) = sqrt(2)/sqrt(2) * 1/sqrt(2) = sqrt(2)*1/sqrt(2)*sqrt(2) = sqrt(2)/sqrt(2)^2 = sqrt(2)/2 = √2 / 2 QED.
1 / sqrt(2) * sqrt(2)/sqrt(2) = sqrt(2) / 2
sqrt(2)/sqrt(2) = 1 ... you can multiply any number by 1 without changing the value, so this method is often used to simplify complex fractions like 1 / sqrt(2)
You have to rationalize the denominator, so 1/sqrt(2) would be multiplied by sqrt(2)/sqrt(2), leaving you with (1*sqrt(2))/(sqrt(2)*sqrt(2)), or sqrt(2)/sqrt(2)^2. In other words, you'd be left with sqrt(2)/2.
You might want to rethink what Root actually means