{
"query": {
"display": "simplificar $$\\sqrt[3]{135}$$",
"symbolab_question": "SIMPLIFY#simplify \\sqrt[3]{135}"
},
"solution": {
"level": "PERFORMED",
"subject": "Algebra",
"topic": "Algebra",
"subTopic": "Simplify",
"default": "3\\sqrt[3]{5}",
"decimal": "5.12992…",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$\\sqrt[3]{135}=3\\sqrt[3]{5}$$",
"input": "\\sqrt[3]{135}",
"steps": [
{
"type": "interim",
"title": "Descomposición en factores primos de $$135:{\\quad}3^{3}\\cdot\\:5$$",
"input": "135",
"steps": [
{
"type": "step",
"primary": "$$135\\:$$divida por $$3\\quad\\:135=45\\cdot\\:3$$",
"result": "=3\\cdot\\:45"
},
{
"type": "step",
"primary": "$$45\\:$$divida por $$3\\quad\\:45=15\\cdot\\:3$$",
"result": "=3\\cdot\\:3\\cdot\\:15"
},
{
"type": "step",
"primary": "$$15\\:$$divida por $$3\\quad\\:15=5\\cdot\\:3$$",
"result": "=3\\cdot\\:3\\cdot\\:3\\cdot\\:5"
},
{
"type": "step",
"primary": "$$3,\\:5$$ son números primos, por lo tanto, no se pueden factorizar mas",
"result": "=3\\cdot\\:3\\cdot\\:3\\cdot\\:5"
},
{
"type": "step",
"result": "=3^{3}\\cdot\\:5"
}
],
"meta": {
"solvingClass": "Composite Integer",
"interimType": "Prime Fac 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRvTIRluRNPwUULD5JCqpmdx9OIb4SEzXKL2fcEuAFVBp4uJ0ZWNYOygXHyq2UMWO5vscSJG68wshcp3OggJfeZG7sZ2xO3Rv22TO2jyZs5OI3RY5Npt8gj+WbFxe9bZTzA=="
}
},
{
"type": "step",
"result": "=\\sqrt[3]{3^{3}\\cdot\\:5}"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$\\sqrt[n]{ab}=\\sqrt[n]{a}\\sqrt[n]{b},\\:\\quad\\:a\\ge0,\\:b\\ge0$$",
"secondary": [
"$$\\sqrt[3]{3^{3}\\cdot\\:5}=\\sqrt[3]{3^{3}}\\sqrt[3]{5}$$"
],
"result": "=\\sqrt[3]{3^{3}}\\sqrt[3]{5}"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$\\sqrt[n]{a^n}=a,\\:\\quad\\:a\\ge0$$",
"secondary": [
"$$\\sqrt[3]{3^{3}}=3$$"
],
"result": "=3\\sqrt[3]{5}"
}
],
"meta": {
"solvingClass": "Solver2"
}
},
"meta": {
"showVerify": true
}
}
Solución
simplificar
Solución
+1
Decimal
Pasos de solución
Descomposición en factores primos de
Aplicar las leyes de los exponentes:
Aplicar las leyes de los exponentes: