{
"query": {
"display": "simplificar $$\\sqrt{4y^{2}}-\\sqrt{5x^{3}}-\\sqrt{3xy}$$",
"symbolab_question": "SIMPLIFY#simplify \\sqrt{4y^{2}}-\\sqrt{5x^{3}}-\\sqrt{3xy}"
},
"solution": {
"level": "PERFORMED",
"subject": "Algebra",
"topic": "Algebra",
"subTopic": "Simplify",
"default": "2y-\\sqrt{5}x\\sqrt{x}-\\sqrt{3xy}",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "Simplificar $$\\sqrt{4y^{2}}-\\sqrt{5x^{3}}-\\sqrt{3xy}:{\\quad}2y-\\sqrt{5}x\\sqrt{x}-\\sqrt{3xy}$$",
"input": "\\sqrt{4y^{2}}-\\sqrt{5x^{3}}-\\sqrt{3xy}",
"steps": [
{
"type": "interim",
"title": "$$\\sqrt{4y^{2}}=2y$$",
"input": "\\sqrt{4y^{2}}",
"steps": [
{
"type": "step",
"primary": "Aplicar la siguiente propiedad de los radicales: $$\\sqrt{ab}=\\sqrt{a}\\sqrt{b},\\:\\quad$$asumiendo que $$a\\ge0,\\:b\\ge0$$",
"secondary": [
"$$\\sqrt{4y^{2}}=\\sqrt{4}\\sqrt{y^{2}}$$"
],
"result": "=\\sqrt{4}\\sqrt{y^{2}}",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
},
{
"type": "interim",
"title": "$$\\sqrt{4}=2$$",
"input": "\\sqrt{4}",
"steps": [
{
"type": "step",
"primary": "Descomponer el número en factores primos: $$4=2^{2}$$",
"result": "=\\sqrt{2^{2}}"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$\\sqrt{a^2}=a,\\:\\quad\\:a\\ge0$$",
"secondary": [
"$$\\sqrt{2^{2}}=2$$"
],
"result": "=2"
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Solver2",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7RnzZTJ4FPnsHVA8/0U5Nl913jtrSFDx+UNsawjlOjV3jAewWnbvHwHHNJ9dhy4+WcubCnYZOJ5L8/2gsdymw1DH70PdnXJfHf+8MsVWHq0c="
}
},
{
"type": "step",
"result": "=2\\sqrt{y^{2}}"
},
{
"type": "step",
"primary": "Aplicar la siguiente propiedad de los radicales: $$\\sqrt{a^2}=a,\\:\\quad$$asumiendo que $$a\\ge0$$",
"secondary": [
"$$\\sqrt{y^{2}}=y$$"
],
"result": "=2y",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
}
],
"meta": {
"interimType": "N/A"
}
},
{
"type": "interim",
"title": "$$\\sqrt{5x^{3}}=\\sqrt{5}x\\sqrt{x}$$",
"input": "\\sqrt{5x^{3}}",
"steps": [
{
"type": "step",
"primary": "Aplicar la siguiente propiedad de los radicales: $$\\sqrt{ab}=\\sqrt{a}\\sqrt{b},\\:\\quad$$asumiendo que $$a\\ge0,\\:b\\ge0$$",
"secondary": [
"$$\\sqrt{5x^{3}}=\\sqrt{5}\\sqrt{x^{3}}$$"
],
"result": "=\\sqrt{5}\\sqrt{x^{3}}",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
},
{
"type": "interim",
"title": "Simplificar $$\\sqrt{x^{3}}:{\\quad}x\\sqrt{x}$$",
"input": "\\sqrt{x^{3}}",
"steps": [
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$a^{b+c}=a^b\\cdot\\:a^c$$",
"secondary": [
"$$x^{2+1}=x^{2}x$$"
],
"result": "=\\sqrt{x^{2}x}",
"meta": {
"practiceLink": "/practice/exponent-practice",
"practiceTopic": "Expand FOIL"
}
},
{
"type": "step",
"primary": "Aplicar la siguiente propiedad de los radicales: $$\\sqrt{ab}=\\sqrt{a}\\sqrt{b},\\:\\quad$$asumiendo que $$a\\ge0,\\:b\\ge0$$",
"secondary": [
"$$\\sqrt{x^{2}x}=\\sqrt{x^{2}}\\sqrt{x}$$"
],
"result": "=\\sqrt{x^{2}}\\sqrt{x}",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
},
{
"type": "step",
"primary": "Aplicar la siguiente propiedad de los radicales: $$\\sqrt{a^2}=a,\\:\\quad$$asumiendo que $$a\\ge0$$",
"secondary": [
"$$\\sqrt{x^{2}}=x$$"
],
"result": "=x\\sqrt{x}",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
}
],
"meta": {
"solvingClass": "Solver2",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7k3PvqMUQ8+Y26Xc5S76fmi061ljBSPJeENOw2efoSWtnZg/z0NUzR4mI/p3WGtp5VxdYPgi3BkP8D39vhVH0ih429vuTSxWa7B/X3D1oP01TliuEXUMQCi7FSsQpz3SxbvydNjzzbgpBjZpEKyF5pg=="
}
},
{
"type": "step",
"result": "=\\sqrt{5}x\\sqrt{x}"
}
],
"meta": {
"interimType": "N/A"
}
},
{
"type": "step",
"result": "=2y-\\sqrt{5}x\\sqrt{x}-\\sqrt{3xy}"
}
],
"meta": {
"solvingClass": "Solver2"
}
},
"meta": {
"showVerify": true
}
}
Solución
simplificar
Solución
Pasos de solución