Recognize Simplification: Simplify the expression $(1)/(sqrt{12})$. First, recognize that $sqrt{12}$ can be simplified because 12 is not a prime number and has square factors.Factorize 12: Factor 12 into its prime factors to find squares that can be taken out of the square root. $12 = 2^2 * 3$.Rewrite Square Root: Rewrite $sqrt{12}$ using the prime factorization. $sqrt{12} = sqrt{2^2 * 3}$.Take Out Square Root: Take the square root of the perfect square $2^2$ out of the square root. $sqrt{2^2 * 3} = 2 * sqrt{3}$.Divide by Simplified Root: Now, simplify the original expression by dividing 1 by $2 * sqrt{3}$. $(1)/(sqrt{12}) = (1)/(2 * sqrt{3})$.Rationalize Denominator: To rationalize the denominator, multiply the numerator and the denominator by $sqrt{3}$. $(1)/(2 * sqrt{3}) * (sqrt{3})/(sqrt{3}) = (sqrt{3})/(2 * 3)$.Simplify Denominator: Simplify the denominator. $(sqrt{3})/(2 * 3) = (sqrt{3})/6$.Final Simplification: The expression is now fully simplified. $(1)/(sqrt{12}) = (sqrt{3})/6$.

Precalculus

Evaluate rational exponents

Full solution

Q. (iii)

\frac{1}{\sqrt{12}}

Recognize Simplification: Simplify the expression $(1)/(sqrt{12})$ . $\newline$ First, recognize that $sqrt{12}$ can be simplified because $12$ is not a prime number and has square factors.
Factorize $12$ : Factor $12$ into its prime factors to find squares that can be taken out of the square root. $\newline$ $12 = 2^2 * 3$ .
Rewrite Square Root: Rewrite $sqrt{12}$ using the prime factorization. $\newline$ $sqrt{12} = sqrt{2^2 * 3}$ .
Take Out Square Root: Take the square root of the perfect square $2^2$ out of the square root. $\newline$ $sqrt{2^2 * 3} = 2 * sqrt{3}$ .
Divide by Simplified Root: Now, simplify the original expression by dividing $1$ by $2 * sqrt{3}$ . $\newline$ $(1)/(sqrt{12}) = (1)/(2 * sqrt{3})$ .
Rationalize Denominator: To rationalize the denominator, multiply the numerator and the denominator by $sqrt{3}$ . $\newline$ $(1)/(2 * sqrt{3}) * (sqrt{3})/(sqrt{3}) = (sqrt{3})/(2 * 3)$ .
Simplify Denominator: Simplify the denominator. $\newline$ $(sqrt{3})/(2 * 3) = (sqrt{3})/6$ .
Final Simplification: The expression is now fully simplified. $\newline$ $(1)/(sqrt{12}) = (sqrt{3})/6$ .