Question

Solve the given equation. $$\sqrt{y}=10$$

   Solve the given equation.
$$\sqrt{y}=10$$

Understanding Elementary Algebra with Geometry

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur… 6th Edition

Chapter 10, Problem 2

Instant Answer

Solved by Expert Ernest Castorena

06/23/2020

Step 1

To remove the square root, we can square both sides of the equation. Show more…

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Solve the given equation. $$\sqrt{y}=10$$

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Key Concepts

Square Root Function

The square root function takes a non-negative input and returns a non-negative value whose square gives the original number. Understanding this function is essential to recognize that it has an inverse operation, namely squaring, which can be used to eliminate the square root in equations.

Inverse Operations

Inverse operations are fundamental in algebra as they allow one to 'undo' an operation. In the context of solving an equation involving a square root, squaring both sides of the equation is the inverse operation that cancels the square root, thereby simplifying the equation and making it more straightforward to isolate and solve for the variable.

Algebraic Manipulation

Algebraic manipulation involves the systematic use of operations such as multiplication, division, addition, subtraction, and exponentiation to isolate and solve for variables in equations. The process of squaring both sides of an equation to remove a square root falls under this concept, enabling the transformation of the equation into a simpler form that can be directly solved.

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