Example Question - square root function
Here are examples of questions we've helped users solve.
Finding the Domain of a Function with a Square Root
Para encontrar el dominio de la función f(x) = 3 / √(x - 3), necesitamos identificar todos los valores de x para los cuales la función está definida. La única restricción aquí es que el denominador no puede ser cero y debe ser un número real, lo que significa que x - 3 debe ser positivo porque la raíz cuadrada de un número negativo no está definida en el conjunto de los números reales. Por lo tanto, configuramos la desigualdad: x - 3 > 0 Resolvemos para x: x > 3 Esto significa que el dominio de f(x) son todos los valores de x mayores que 3. En notación de intervalo, el dominio se escribe como: (3, +∞) En resumen, el dominio de la función f(x) = 3 / √(x - 3) es todos los valores reales de x mayores que 3.
Simplifying Radical Expressions
To simplify the radical expression \( \sqrt{48x^{13}y^9} \), you'll need to break down the numbers and variables inside the radical into factors that are perfect squares, as the square root function will cancel with squared terms. First, factor the number 48 and express it as a product of squared numbers: 48 = 16 * 3, where 16 is a perfect square (since 16 = 4^2). Next, for the variable terms \( x^{13} \) and \( y^9 \), we want to find the highest even powers since they can be taken out of the square root as a single power. For \( x^{13} \), the highest even power less than 13 is 12, which can be written as \( (x^6)^2 \). For \( y^9 \), the highest even power less than 9 is 8, which can be written as \( (y^4)^2 \). The expression becomes: \( \sqrt{16*3*(x^6)^2*(y^4)^2} \) Taking the square roots of the perfect squares, we get: \( 4x^6y^4\sqrt{3} \) So the simplified form of the radical expression \( \sqrt{48x^{13}y^9} \) is \( 4x^6y^4\sqrt{3} \).
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