Solve the Square Root Equation: √x = 15

Q: Why do I square both sides instead of doing something else?

Squaring is the inverse operation of taking a square root! Just like addition and subtraction cancel each other out, $ (\sqrt{x})^2 $ simplifies to just x.

Q: How do I calculate 15² quickly?

Remember that $ 15^2 = 15 \times 15 $. You can think of it as $ (10 + 5)^2 $ or just multiply: 15 × 15 = 225.

Q: What if the square root equals a negative number?

Square roots of real numbers are always positive or zero! If you see $ \sqrt{x} = -5 $, there's no real solution because square roots can't be negative.

Q: How can I check my answer is definitely right?

Substitute your answer back into the original equation. For $ x = 225 $: does $ \sqrt{225} = 15 $? Since $ 15 \times 15 = 225 $, yes it does!

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

00:10 Square and root cancel each other out

00:15 Break down the exponent 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

$\sqrt{x}=15$

2

Step-by-step solution

To solve the given problem, we will follow these steps:

Step 1: Square both sides of the equation
Step 2: Simplify to find $x$

Now, let's work through each step:

Step 1: We are given $\sqrt{x} = 15$ .
To eliminate the square root, square both sides of the equation:

(\sqrt{x})^2 = 15^2

Step 2: Simplify both sides:
On the left, $(\sqrt{x})^2 = x$ .
On the right, $15^2 = 225$ .

This gives us the equation:

x = 225

Thus, the solution to the problem is $\boxed{225}$ .

3

Final Answer

225

Key Points to Remember

Essential concepts to master this topic

Rule: Square both sides to eliminate the square root symbol
Technique: $(\sqrt{x})^2 = 15^2$ becomes $x = 225$
Check: Substitute back: $\sqrt{225} = 15$ since $15 \times 15 = 225$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting the number instead of squaring
Don't try to solve $\sqrt{x} = 15$ by adding 15 to both sides = wrong operation! This doesn't eliminate the square root and leads to nonsensical equations. Always square both sides to remove the radical symbol.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why do I square both sides instead of doing something else?

+

Squaring is the inverse operation of taking a square root! Just like addition and subtraction cancel each other out, $(\sqrt{x})^2$ simplifies to just x.

How do I calculate 15² quickly?

+

Remember that $15^2 = 15 \times 15$ . You can think of it as $(10 + 5)^2$ or just multiply: 15 × 15 = 225.

What if the square root equals a negative number?

+

Square roots of real numbers are always positive or zero! If you see $\sqrt{x} = -5$ , there's no real solution because square roots can't be negative.

Do I always get one answer for these equations?

+

For basic square root equations like this one, yes! Once you isolate the square root and square both sides, you get one positive solution.

How can I check my answer is definitely right?

+

Substitute your answer back into the original equation. For $x = 225$ : does $\sqrt{225} = 15$ ? Since $15 \times 15 = 225$ , yes it does!

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Solve the Square Root Equation: √x = 15

Square Root Equations with Basic Isolation

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I square both sides instead of doing something else?

How do I calculate 15² quickly?

What if the square root equals a negative number?

Do I always get one answer for these equations?

How can I check my answer is definitely right?

🌟 Unlock Your Math Potential

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