You supply the $\pm$

SAT Glossary

The rule separating x^2=49 (two solutions, ±7) from √(49) (one number, 7): the ± is supplied by you when you apply a square root to solve an equation, never by the symbol, which has already committed to the positive branch. Items offering '±7' for √(49) and '7' for x^2=49 test the same distinction from opposite sides, and both appear. Desmos will mislead you here — it returns the principal root and will not remind you of the second solution.

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for $\\sqrt{49}$ and '7' for $x^2=49$ test the same distinction from opposite sides, and both appear. Desmos will mislead you here — it returns the principal root and will not remind you of the second solution.","section":"Mathematics","source":"KomFi SAT vF - Chapter 38: Radicals and Rational Exponents","necessity":4,"learnMore":"This distinguishes two situations that look similar but behave differently: solving the equation $x^2=49$ by taking a square root gives you TWO solutions, $\\pm7$ (both $7^2=49$ and $(-7)^2=49$ are true) — and that plus-or-minus symbol is something YOU have to add yourself when you take a square root to SOLVE an equation. But the expression $\\sqrt{49}$ all by itself, with no equation to solve, is defined to mean just ONE single number: positive 7 — the radical symbol has already committed to only the positive branch, no exceptions. The test likes to offer '$\\pm7

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as a wrong answer for plain $\\sqrt{49}$, and offer just '7' as a wrong (incomplete) answer for the equation $x^2=49$ — testing the exact same distinction from both directions at once. Watch out for graphing calculators like Desmos here too: they'll only ever show you the principal (positive) root and won't remind you that a second solution exists.","courseId":"sat","publicSeo":true,"seoSlug":"you-supply-the-1fjv6p"}

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KomFi Academy is a curated training platform with 66,000+ practice questions, 25,000+ flashcards, on-demand video lectures, podcasts, and 4K slide decks across the topics serious professionals study: GMAT, LSAT, MCAT, SAT, Investment Banking, Private Equity (LBOs & PE math), Private Credit, Quantitative Finance, Financial Accounting, Asset- Backed Securities, Volume Profile Analysis, Order Flow Trading, Market Microstructure, Volume Spread Analysis, Elliott Wave Theory, Volume-Price Analysis, and Public Offering Frameworks.

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