simplify sqrt(4y^2)-sqrt(5x^3)-sqrt(3xy)

{ "query": { "display": "simplify $$\\sqrt{4y^{2}}-\\sqrt{5x^{3}}-\\sqrt{3xy}$$", "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": "Simplify $$\\sqrt{4y^{2}}-\\sqrt{5x^{3}}-\\sqrt{3xy}:{\\quad}2y-\\sqrt{5}x\\sqrt{x}-\\sqrt{3xy}$$", "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": "Apply radical rule: $$\\sqrt{ab}=\\sqrt{a}\\sqrt{b},\\:\\quad$$ assuming $$a\\ge0,\\:b\\ge0$$", "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": "Factor the number: $$4=2^{2}$$", "result": "=\\sqrt{2^{2}}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad\\:a\\ge0$$", "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": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad$$ assuming $$a\\ge0$$", "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": "Apply radical rule: $$\\sqrt{ab}=\\sqrt{a}\\sqrt{b},\\:\\quad$$ assuming $$a\\ge0,\\:b\\ge0$$", "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": "Simplify $$\\sqrt{x^{3}}:{\\quad}x\\sqrt{x}$$", "input": "\\sqrt{x^{3}}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^{b+c}=a^b\\cdot\\:a^c$$", "secondary": [ "$$x^{2+1}=x^{2}x$$" ], "result": "=\\sqrt{x^{2}x}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{ab}=\\sqrt{a}\\sqrt{b},\\:\\quad$$ assuming $$a\\ge0,\\:b\\ge0$$", "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": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad$$ assuming $$a\\ge0$$", "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/X3D1oP01iqQ92o12CYXtePqkgOt2E9+pQzkeUU8I2pnPLEPo8vQ==" } }, { "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 } }