simplify sqrt(-100)

{ "query": { "display": "simplify $$\\sqrt{-100}$$", "symbolab_question": "SIMPLIFY#simplify \\sqrt{-100}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "10i", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Simplify $$\\sqrt{-100}:{\\quad}10i$$", "input": "\\sqrt{-100}", "steps": [ { "type": "step", "primary": "Apply radical rule: $$\\sqrt{-a}=\\sqrt{a}\\sqrt{-1}$$", "secondary": [ "$$\\sqrt{-100}=\\sqrt{100}\\sqrt{-1}$$" ], "result": "=\\sqrt{100}\\sqrt{-1}", "meta": { "practiceLink": "/practice/radicals-practice", "practiceTopic": "Radical Rules" } }, { "type": "step", "primary": "Apply imaginary number rule: $$\\sqrt{-1}=i$$", "result": "=\\sqrt{100}i", "meta": { "practiceLink": "/practice/complex-numbers-practice", "practiceTopic": "Expand FOIL" } }, { "type": "interim", "title": "$$\\sqrt{100}=10$$", "input": "\\sqrt{100}", "steps": [ { "type": "step", "primary": "Factor the number: $$100=10^{2}$$", "result": "=\\sqrt{10^{2}}" }, { "type": "step", "primary": "Apply radical rule: $$\\sqrt{a^2}=a,\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\sqrt{10^{2}}=10$$" ], "result": "=10" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7RW6oBYmo5Js74GBIV6upv96GQqufR6tr2vPxOUv7H+8Khqe7+dajLA9h/DZSrCk/hj6ylSwHjJkmQPKH34+7f95LNcObF6QhiI8u0x4Pxok=" } }, { "type": "step", "result": "=10i" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }