simplify (sqrt(6)+sqrt(3))(sqrt(6)-sqrt(3))

{ "query": { "display": "simplify $$\\left(\\sqrt{6}+\\sqrt{3}\\right)\\left(\\sqrt{6}-\\sqrt{3}\\right)$$", "symbolab_question": "SIMPLIFY#simplify (\\sqrt{6}+\\sqrt{3})(\\sqrt{6}-\\sqrt{3})" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "3", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left(\\sqrt{6}+\\sqrt{3}\\right)\\left(\\sqrt{6}-\\sqrt{3}\\right)=3$$", "input": "\\left(\\sqrt{6}+\\sqrt{3}\\right)\\left(\\sqrt{6}-\\sqrt{3}\\right)", "steps": [ { "type": "interim", "title": "Apply Difference of Two Squares $$\\left(\\sqrt{6}+\\sqrt{3}\\right)\\left(\\sqrt{6}-\\sqrt{3}\\right):{\\quad}3$$", "input": "\\left(\\sqrt{6}+\\sqrt{3}\\right)\\left(\\sqrt{6}-\\sqrt{3}\\right)", "steps": [ { "type": "step", "primary": "Apply Difference of Two Squares Formula: $$\\left(a+b\\right)\\left(a-b\\right)=a^2-b^2$$", "secondary": [ "$$\\left(\\sqrt{6}+\\sqrt{3}\\right)\\left(\\sqrt{6}-\\sqrt{3}\\right)=\\left(\\sqrt{6}\\right)^{2}-\\left(\\sqrt{3}\\right)^{2}$$" ], "result": "=\\left(\\sqrt{6}\\right)^{2}-\\left(\\sqrt{3}\\right)^{2}", "meta": { "practiceLink": "/practice/expansion-practice#area=main&subtopic=Difference%20of%20Two%20Squares", "practiceTopic": "Expand Difference of Squares" } }, { "type": "interim", "title": "$$\\left(\\sqrt{6}\\right)^{2}-\\left(\\sqrt{3}\\right)^{2}=3$$", "input": "\\left(\\sqrt{6}\\right)^{2}-\\left(\\sqrt{3}\\right)^{2}", "steps": [ { "type": "interim", "title": "$$\\left(\\sqrt{6}\\right)^{2}=6$$", "input": "\\left(\\sqrt{6}\\right)^{2}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(\\sqrt[n]{a}\\right)^n=a,\\:\\quad\\:n\\:is\\:odd\\:or\\:a\\ge0$$", "secondary": [ "$$\\left(\\sqrt{6}\\right)^{2}=6$$" ], "result": "=6" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "$$\\left(\\sqrt{3}\\right)^{2}=3$$", "input": "\\left(\\sqrt{3}\\right)^{2}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(\\sqrt[n]{a}\\right)^n=a,\\:\\quad\\:n\\:is\\:odd\\:or\\:a\\ge0$$", "secondary": [ "$$\\left(\\sqrt{3}\\right)^{2}=3$$" ], "result": "=3" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "=6-3" }, { "type": "step", "primary": "Subtract the numbers: $$6-3=3$$", "result": "=3" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7srZuGI+Q8Iw6MX6TyHGHi+WPArc7xY0IxZSZu7y2Zgt8kR7hsO/rTOTBE0w4+r1RDEk3voRBBK9vivW91vSZBvEq6qw1uJhXBCvoTzamTfK7bUBrjhrqFo0RLSNuxF0HMIWuby8K8tnFmx1jg0tBW7CI2sSeA74029n2yo277ZU=" } }, { "type": "step", "result": "=3" } ], "meta": { "solvingClass": "Solver2", "interimType": "Expand Difference Squares Rule Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7O62yKKtC6+yKjUNmPFBt9xM1EqX1OyG1IpLqJdZHHeSkzsQJTJhEPBh+3NL35NoMwOpo8vUUvLLL2mDB+OFvre25PML1lLl1PzxGfQkFIDnBuraI4/iX7DKKWSw+OSlX9jQwH7MiGgmfdkO3YY/2S0PgY1mHqDA7G0GAnH+0zqZSBv6izheLVUKQ/emokAUypXxec6cLVXRf1BA6DUS7FmaY/SbCxu6YYy/vKEYZf1a2T5jY20Cc8ISbRq20lWxRkmIl+ntHI6/85Y38SLuQDPiL4WvteTtttnlm0cCdH6A=" } }, { "type": "step", "result": "=3" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }