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35:["$","div",null,{"className":"bg-white rounded-lg shadow-sm p-8","children":[["$","h2",null,{"className":"typo-large mb-6 text-mist-950","children":"Frequently Asked Questions"}],["$","div",null,{"className":"space-y-6","children":[["$","div","0",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What is the nth root of a number?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The nth root of a number is a value that, when multiplied by itself n times, gives you the original number. For example, the 4th root of 16 is 2, because 2 × 2 × 2 × 2 = 16. It's the inverse operation of raising a number to a power.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","1",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What is the formula for nth root?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The nth root formula is: ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"ⁿ√x = x^(1/n)","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"To find any root, raise your number to the power of 1 divided by the root index. For a 4th root, that's x^(1/4) or x^0.25. For a cube root, it's x^(1/3) or x^0.333.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","2",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"How do I calculate nth root without a calculator?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"You can estimate by finding the nearest perfect roots. For the 4th root of 80, you know 3⁴ = 81 and 2⁴ = 16, so the answer is just under 3 (about 2.99). For precise answers without a calculator, you'd need to use logarithms or iterative methods—but for most purposes, bracketing gives you a close enough estimate.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","3",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What's the difference between a root and an exponent?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Roots and exponents are inverse operations—opposites of each other. If 2⁴ = 16 (exponent), then ⁴√16 = 2 (root). Exponents multiply a number by itself; roots find what number was multiplied. They're two sides of the same mathematical coin.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","4",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"Can you find the nth root of a negative number?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"It depends on the root. Odd roots of negative numbers work fine: the cube root of -27 is -3, because (-3) × (-3) × (-3) = -27. Even roots of negative numbers don't have real solutions—there's no real number that multiplies by itself an even number of times to give a negative result.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],"$L37","$L38","$L39","$L3a","$L3b"]}]]}]
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37:["$","div","5",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What is the 4th root of 16?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The 4th root of 16 is ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"2","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":". You can verify this: 2 × 2 × 2 × 2 = 16. This is a perfect 4th root because the answer is a whole number.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
38:["$","div","6",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"How do I find the nth root on a TI-84?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Press ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"MATH","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":", then select option ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"5: ˣ√","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":". Enter the root index first, press MATH and select 5 again, enter your number, then press ENTER. Alternatively, use the exponent method: enter your number, press ^, then enter (1/n), and press ENTER. The exponent method actually works on more calculator models.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
39:["$","div","7",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What is a radical vs. a root?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"They're the same thing—just different terminology. \"Radical\" refers to the symbol (√) and \"root\" refers to the mathematical operation. The expression ³√27 can be called \"the cube root of 27\" or \"the radical of 27 with index 3.\" In everyday use, most people just say \"root.\"","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
3a:["$","div","8",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"How do I type nth root in Excel or Google Sheets?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Use the POWER function with a fractional exponent. For the 4th root of 67:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Excel/Sheets:","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" ","type":"text","version":1},{"detail":0,"format":16,"mode":"normal","style":"","text":"=POWER(67, 1/4)","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" returns 2.861006","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Alternative:","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" ","type":"text","version":1},{"detail":0,"format":16,"mode":"normal","style":"","text":"=67^(1/4)","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" works the same way","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Both methods give identical results—use whichever feels more natural to you.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
3b:["$","div","9",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"When would I need a 5th root or higher?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Higher roots appear in finance (CAGR calculations), statistics (geometric means), engineering (dimensional analysis), and physics. For example, calculating the average annual return of an investment over 5 years requires a 5th root. They're less common than square or cube roots, but essential when they come up.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
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