Calculate the Square Root: Solving √144 Step by Step

Q: How do I know if a number is a perfect square?

A perfect square is a number that equals some integer times itself. Try multiplying small numbers: 10×10=100, 11×11=121, 12×12=144. With practice, you'll recognize common perfect squares!

Q: What if I don't remember that 12×12=144?

You can work systematically! Start with 10×10=100 (too small), then 11×11=121 (still too small), then 12×12=144 (perfect match!).

Q: Is there always only one answer for square roots?

For basic math, we use the principal (positive) square root. While technically both 12 and -12 when squared equal 144, $ \sqrt{144} $ means the positive answer: 12.

Q: What if the number isn't a perfect square?

Some square roots like $ \sqrt{150} $ don't have nice whole number answers. For now, focus on perfect squares like 144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, and 1.

Q: Why can't I use a calculator for this?

Learning to recognize perfect squares builds number sense and speeds up your math! Once you know $ 12^2 = 144 $, you instantly know $ \sqrt{144} = 12 $ without any calculation.

Perfect Square Roots with Recognition Skills

$\sqrt{144}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this math problem step by step.

00:09 The square root of a number, X, squared is simply X. The root and the square cancel each other out.

00:19 For example, the number 144 can be broken down into 12 squared.

00:25 We're going to use this concept in our exercise.

00:29 And that's the solution to the question! Great job.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{144}=$

Step-by-step solution

To solve this problem, we proceed with the following steps:

Step 1: Identify that the problem asks for the square root of 144.
Step 2: Use the concept of square roots, where $\sqrt{n} = x$ implies $x^2 = n$ .
Step 3: Check for a perfect square whose square equals 144.

Now, let's solve the problem:

Step 1: We need the square root $\sqrt{144}$ .

Step 2: Recall that $x^2 = 144$ . We need to find $x$ .

Step 3: Recognize that 144 is a perfect square and find $x$ such that $x^2 = 144$ . Through either calculation or prior knowledge, we know:
$12^2 = 144$ .

Therefore, the square root of 144 is $\sqrt{144} = 12$ .

Thus, the solution to the problem is $\mathbf{12}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root asks which number multiplied by itself equals 144
Technique: Recognize 144 as perfect square: $12^2 = 12 \times 12 = 144$
Check: Verify answer by squaring: $12^2 = 144$ confirms $\sqrt{144} = 12$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division
Don't divide 144 by 2 to get 72 = wrong answer! This confuses square roots with simple division. Always ask 'what number times itself equals 144?' not 'what is 144 divided by something?'

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I know if a number is a perfect square?

A perfect square is a number that equals some integer times itself. Try multiplying small numbers: 10×10=100, 11×11=121, 12×12=144. With practice, you'll recognize common perfect squares!

What if I don't remember that 12×12=144?

You can work systematically! Start with 10×10=100 (too small), then 11×11=121 (still too small), then 12×12=144 (perfect match!).

Is there always only one answer for square roots?

For basic math, we use the principal (positive) square root. While technically both 12 and -12 when squared equal 144, $\sqrt{144}$ means the positive answer: 12.

What if the number isn't a perfect square?

Some square roots like $\sqrt{150}$ don't have nice whole number answers. For now, focus on perfect squares like 144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, and 1.

Why can't I use a calculator for this?

Learning to recognize perfect squares builds number sense and speeds up your math! Once you know $12^2 = 144$ , you instantly know $\sqrt{144} = 12$ without any calculation.

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