Solve the Square Root Equation: √x = 12

Square Root Equations with Perfect Square Solutions

x=12 \sqrt{x}=12

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 Square both sides to isolate X
00:09 Square and root cancel each other out
00:17 Break down the power into multiplication and calculate
00:21 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

x=12 \sqrt{x}=12

2

Step-by-step solution

To solve the equation x=12 \sqrt{x} = 12 , we need to eliminate the square root by squaring both sides.

Let's follow these steps:

  • Step 1: Square both sides of the equation to remove the square root:

(x)2=122 (\sqrt{x})^2 = 12^2

  • Step 2: Simplify the squared terms:

x=144 x = 144

Therefore, the value of x x that satisfies the equation is 144 \boxed{144} .

Confirming with the choices given, the correct answer is 144, which matches choice 2.

3

Final Answer

144

Key Points to Remember

Essential concepts to master this topic
  • Rule: Square both sides to eliminate the square root symbol
  • Technique: (x)2=122 (\sqrt{x})^2 = 12^2 becomes x=144 x = 144
  • Check: Substitute back: 144=12 \sqrt{144} = 12 confirms our answer ✓

Common Mistakes

Avoid these frequent errors
  • Squaring only one side of the equation
    Don't square just x \sqrt{x} to get x = 12! This ignores the equation balance and gives the wrong answer. Always square both sides equally to maintain the equation: (x)2=122 (\sqrt{x})^2 = 12^2 .

Practice Quiz

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\( 11^2= \)

FAQ

Everything you need to know about this question

Why do we square both sides instead of just removing the square root?

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You can't just "remove" a square root! The square root and squaring are inverse operations, so squaring both sides cancels out the square root while keeping the equation balanced.

What if I get a negative number under the square root?

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In basic algebra, we only work with real numbers, so x \sqrt{x} requires x≥0 x \geq 0 . Since our answer is 144 (positive), we're all good!

How do I know 144 is a perfect square?

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A perfect square is a number that equals some integer times itself. Since 12×12=144 12 \times 12 = 144 , we know 144 is a perfect square and 144=12 \sqrt{144} = 12 .

Do I always get whole number answers for square root equations?

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Not always! This problem has a perfect square answer, but many square root equations have decimal or irrational answers. Always check your work by substituting back.

What's the difference between √x = 12 and x² = 12?

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These are completely different equations! x=12 \sqrt{x} = 12 gives x=144 x = 144 , while x2=12 x^2 = 12 gives x=±12 x = \pm\sqrt{12} .

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