Math Problem Statement

ome Solve Square Root Equation √(x + 5) = 8 find x

Solution

To solve the equation:

x+5=8\sqrt{x + 5} = 8

Follow these steps:

  1. Square both sides to eliminate the square root:

(x+5)2=82(\sqrt{x + 5})^2 = 8^2

This simplifies to:

x+5=64x + 5 = 64

  1. Solve for xx:

x=645x = 64 - 5

x=59x = 59

So, the solution is x=59x = 59.

Would you like a more detailed explanation, or do you have any questions?


Here are some related questions:

  1. How do you solve square root equations with different constants?
  2. What if the equation had a negative result under the square root?
  3. How would you solve a square root equation with variables on both sides?
  4. What happens when you square both sides of an equation in general?
  5. How do you check if a solution is valid for a square root equation?

Tip: Always check the solution in the original equation to ensure it doesn't introduce extraneous solutions.

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Math Problem Analysis

Mathematical Concepts

Square Root Equations
Basic Algebra

Formulas

√(x + 5) = 8
(√(x + 5))^2 = 8^2

Theorems

Properties of Square Roots
Basic Algebraic Manipulation

Suitable Grade Level

Grades 8-10