simplify \sqrt[3]{135}

{ "query": { "display": "simplify $$\\sqrt[3]{135}$$", "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": "Prime factorization of $$135:{\\quad}3^{3}\\cdot\\:5$$", "input": "135", "steps": [ { "type": "step", "primary": "$$135\\:$$divides by $$3\\quad\\:135=45\\cdot\\:3$$", "result": "=3\\cdot\\:45" }, { "type": "step", "primary": "$$45\\:$$divides by $$3\\quad\\:45=15\\cdot\\:3$$", "result": "=3\\cdot\\:3\\cdot\\:15" }, { "type": "step", "primary": "$$15\\:$$divides by $$3\\quad\\:15=5\\cdot\\:3$$", "result": "=3\\cdot\\:3\\cdot\\:3\\cdot\\:5" }, { "type": "step", "primary": "$$3,\\:5$$ are all prime numbers, therefore no further factorization is possible", "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+ZU0OMrfn8NOj0LUzuzje6xTyxRvTIRluRNPwUULD5JCqpmdx9OIb4SEzXKL2fcEuAFVBp9NqQ+lATTQCpcI1REFC/BKGFkX1ACFJO8XX3CmdEmA0kWZwO1cmVlEhizmNlVkwH" } }, { "type": "step", "result": "=\\sqrt[3]{3^{3}\\cdot\\:5}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt[n]{ab}=\\sqrt[n]{a}\\sqrt[n]{b},\\:\\quad\\:a\\ge0,\\:b\\ge0$$", "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": "Apply radical rule: $$\\sqrt[n]{a^n}=a,\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\sqrt[3]{3^{3}}=3$$" ], "result": "=3\\sqrt[3]{5}" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }