Calculate the Square Root of 169: Basic Radical Evaluation

Q: How do I know 13 is the square root without a calculator?

Try numbers systematically! Since $ 10^2 = 100 $ and $ 15^2 = 225 $, the answer must be between 10 and 15. Test 12: $ 12 \times 12 = 144 $ (too small), then 13: $ 13 \times 13 = 169 $ (perfect!).

Q: What makes 169 a perfect square?

A perfect square is a whole number that equals another whole number multiplied by itself. Since $ 13 \times 13 = 169 $ exactly, 169 is a perfect square with no decimal remainder.

Q: Why isn't the answer -13 since (-13)² also equals 169?

You're mathematically correct that $ (-13)^2 = 169 $, but the square root symbol √ always means the positive square root by convention. We call -13 the negative square root.

Q: What if I can't remember the multiplication tables?

Start with numbers you know! Since $ 10^2 = 100 $ and $ 20^2 = 400 $, try numbers between 10-20. Use trial and error systematically, or break down: $ 13^2 = (10+3)^2 $.

Q: Are there any tricks to recognize perfect squares?

Yes! Perfect squares often end in 0, 1, 4, 5, 6, or 9. Since 169 ends in 9, it could be a perfect square. Also, memorize common squares: $ 1^2, 2^2, 3^2... 15^2 $ for quick recognition.

Square Roots with Perfect Square Recognition

$\sqrt{169}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

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

00:13 We'll break down 169 to 13 squared

00:17 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

$\sqrt{169}=$

Step-by-step solution

To solve for the square root of 169, we need to determine which whole number, when multiplied by itself, equals 169.

Step 1: Recall that squaring a number means multiplying the number by itself. Therefore, we need to find a number $n$ such that $n \times n = 169$ .
Step 2: Check known square values or perform some calculations: $13 \times 13 = 169$ .
Step 3: Verify that $13^2 = 169$ , confirming that 13 is the square root.

Therefore, the solution to the problem is $\sqrt{169} = 13$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root asks what number times itself equals the given value
Recognition: Check if $13 \times 13 = 169$ to find the root
Verification: Square your answer to confirm $13^2 = 169$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with half the number
Don't think √169 = 169 ÷ 2 = 84.5! This completely misunderstands what square root means. Always find the number that when multiplied by itself gives 169.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{36}=$

FAQ

Everything you need to know about this question

How do I know 13 is the square root without a calculator?

Try numbers systematically! Since $10^2 = 100$ and $15^2 = 225$ , the answer must be between 10 and 15. Test 12: $12 \times 12 = 144$ (too small), then 13: $13 \times 13 = 169$ (perfect!).

What makes 169 a perfect square?

A perfect square is a whole number that equals another whole number multiplied by itself. Since $13 \times 13 = 169$ exactly, 169 is a perfect square with no decimal remainder.

Why isn't the answer -13 since (-13)² also equals 169?

You're mathematically correct that $(-13)^2 = 169$ , but the square root symbol √ always means the positive square root by convention. We call -13 the negative square root.

What if I can't remember the multiplication tables?

Start with numbers you know! Since $10^2 = 100$ and $20^2 = 400$ , try numbers between 10-20. Use trial and error systematically, or break down: $13^2 = (10+3)^2$ .

Are there any tricks to recognize perfect squares?

Yes! Perfect squares often end in 0, 1, 4, 5, 6, or 9. Since 169 ends in 9, it could be a perfect square. Also, memorize common squares: $1^2, 2^2, 3^2... 15^2$ for quick recognition.

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