Calculate √961 - √1: Square Root Difference Problem

Q: What if I don't recognize the perfect square?

Try systematic checking! Start with numbers near the square root estimate. For 961, since $ 30^2 = 900 $ and $ 32^2 = 1024 $, test 31: $ 31^2 = 961 $ ✓

Q: Can I use a calculator for square roots?

While calculators help verify answers, recognizing perfect squares is faster and builds number sense. Practice common perfect squares from $ 1^2 $ to $ 40^2 $ for quick recognition!

Q: Why is the answer 30 and not 32?

Be careful with the subtraction! $ \sqrt{961} - \sqrt{1} = 31 - 1 = 30 $. The common error is calculating $ \sqrt{961} $ wrong or making arithmetic mistakes in the final step.

Q: Are there other perfect squares I should memorize?

Yes! Focus on squares from 1 to 25 first: $ 1^2=1, 2^2=4, 3^2=9... 25^2=625 $. Then learn larger ones like $ 31^2=961 $ that appear in problems.

Square Root Calculation with Perfect Squares

$\sqrt{961}-\sqrt{1}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Root of any number (X) squared, root cancels square

00:06 We decompose 961 to 31 squared

00:12 We'll use this formula in our exercise

00:15 Root and square cancel out

00:20 Let's calculate and solve

00:23 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

$\sqrt{961}-\sqrt{1}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate $\sqrt{961}$
Step 2: Calculate $\sqrt{1}$
Step 3: Subtract the square roots obtained in Steps 1 and 2

Now, let's work through each step:
Step 1: We need to find $\sqrt{961}$ . Recognize that 961 is a perfect square and $\sqrt{961} = 31$ because $31^2 = 961$ .
Step 2: Next, calculate $\sqrt{1}$ . Since 1 is also a perfect square, $\sqrt{1} = 1$ .
Step 3: Subtract these values: $31 - 1 = 30$ .

Therefore, the solution to the problem is $30$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perfect Squares: Recognize that 961 and 1 are perfect squares
Technique: Calculate $\sqrt{961} = 31$ since $31^2 = 961$
Check: Verify by squaring: $31^2 = 961$ and $1^2 = 1$ ✓

Common Mistakes

Avoid these frequent errors

Trying to estimate square roots instead of recognizing perfect squares
Don't guess or use approximation methods like $\sqrt{961} ≈ 30$ ! This leads to wrong answers and wastes time. Always check if the number is a perfect square first by testing if any whole number squared equals it.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I know if 961 is a perfect square?

Look for patterns! Since 961 ends in 1, try numbers ending in 1 or 9. Test: $31^2 = 31 \times 31 = 961$ . You can also start from nearby perfect squares like $30^2 = 900$ and work up.

What if I don't recognize the perfect square?

Try systematic checking! Start with numbers near the square root estimate. For 961, since $30^2 = 900$ and $32^2 = 1024$ , test 31: $31^2 = 961$ ✓

Can I use a calculator for square roots?

While calculators help verify answers, recognizing perfect squares is faster and builds number sense. Practice common perfect squares from $1^2$ to $40^2$ for quick recognition!

Why is the answer 30 and not 32?

Be careful with the subtraction! $\sqrt{961} - \sqrt{1} = 31 - 1 = 30$ . The common error is calculating $\sqrt{961}$ wrong or making arithmetic mistakes in the final step.

Are there other perfect squares I should memorize?

Yes! Focus on squares from 1 to 25 first: $1^2=1, 2^2=4, 3^2=9... 25^2=625$ . Then learn larger ones like $31^2=961$ that appear in problems.

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