Calculate the Square Root: Finding √196 Step by Step

Q: How do I know if 196 is a perfect square?

A perfect square is a number that comes from multiplying an integer by itself. Since $ 14 \times 14 = 196 $, we know 196 is a perfect square!

Q: What if I can't remember which number times itself equals 196?

Try numbers systematically! Start with 10 × 10 = 100 (too small), then 15 × 15 = 225 (too big). This tells you the answer is between 10 and 15, so test numbers like 12, 13, 14.

Q: Are there any shortcuts to find square roots?

Memorize common perfect squares: $ 1^2 = 1, 2^2 = 4, 3^2 = 9, ..., 15^2 = 225 $. Knowing these by heart makes square root problems much faster!

Q: What does the square root symbol actually mean?

The symbol $ \sqrt{} $ asks: "What number, when multiplied by itself, gives this result?" So $ \sqrt{196} $ means "what number × itself = 196?"

Q: Can square roots be negative?

In basic math, we use the principal (positive) square root. While (-14) × (-14) = 196 is also true, $ \sqrt{196} = 14 $ by convention means the positive answer.

Perfect Squares with Mental Calculation Methods

$\sqrt{196}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Square root of any number (X) squared, root cancels square

00:12 We'll break down 196 to 14 squared

00:16 We'll use this formula in our exercise

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{196}=$

Step-by-step solution

The given problem requires us to determine the square root of 196. To solve this, we need to find a number that, when multiplied by itself, equals 196.

Let's evaluate whether 196 is a perfect square. We know that:

$14 \times 14 = 196$

Therefore, the square root of 196 is $14$ , since 14 multiplied by itself gives 196.

Thus, the correct answer is $14$ , which corresponds to choice 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perfect Square: A number that equals another integer multiplied by itself
Technique: Test 14 × 14 = 196 to verify the square root
Check: Multiply your answer by itself: 14 × 14 = 196 ✓

Common Mistakes

Avoid these frequent errors

Guessing without checking multiplication
Don't just pick a number that looks close to the answer = wrong result! This wastes time and leads to careless errors. Always multiply your guess by itself to verify it equals the original number.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{36}=$

FAQ

Everything you need to know about this question

How do I know if 196 is a perfect square?

A perfect square is a number that comes from multiplying an integer by itself. Since $14 \times 14 = 196$ , we know 196 is a perfect square!

What if I can't remember which number times itself equals 196?

Try numbers systematically! Start with 10 × 10 = 100 (too small), then 15 × 15 = 225 (too big). This tells you the answer is between 10 and 15, so test numbers like 12, 13, 14.

Are there any shortcuts to find square roots?

Memorize common perfect squares: $1^2 = 1, 2^2 = 4, 3^2 = 9, ..., 15^2 = 225$ . Knowing these by heart makes square root problems much faster!

What does the square root symbol actually mean?

The symbol $\sqrt{}$ asks: "What number, when multiplied by itself, gives this result?" So $\sqrt{196}$ means "what number × itself = 196?"

Can square roots be negative?

In basic math, we use the principal (positive) square root. While (-14) × (-14) = 196 is also true, $\sqrt{196} = 14$ by convention means the positive answer.

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