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Equations with Square Roots Calculator

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Example
Created on 2024-06-20Asked by Victoria Martin (Solvelet student)
Solve the equation x=9 \sqrt{x} = 9 .

Solution

To solve the equation x=9 \sqrt{x} = 9 , square both sides: (x)2=92    x=81. (\sqrt{x})^2 = 9^2 \implies x = 81. \textbf{Note:} Since the square root function always gives the positive square root, x=81 x = 81 is the only solution. Solved on Solvelet with Basic AI Model
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1. Solve the equation x3=5 \sqrt{x - 3} = 5 .2. Find all solutions to the equation 2x+1=x3 \sqrt{2x + 1} = x - 3 .
DefinitionSquare root equation: algebraic or transcendental equations involving radicals or square roots of variables or functions. These would be polynomials, radials, and functional equations, which may or may not have a real root, depending on the domain and functions properties. Square root equations are relevant in various fields such as algebra, geometry, calculus, physics.Whichever is the need, the following techniques usually work: isolate the radical term, square both sides and solve or algebraic manipulations. For example: x​+3=5 is an equation containing a square root. Featured image: Isolate the square root term and square both sides to get x=4.
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