Solve: (√81 × √4)/(√9 × √9) - Square Root Fraction Simplification

Q: Do I need to memorize all perfect squares?

Not all, but knowing common ones helps! Focus on perfect squares up to 144: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. These appear frequently in problems.

Q: Can I use a calculator for square roots?

For perfect squares like $ \sqrt{81} $, try to recognize them mentally first. Calculators are helpful for non-perfect squares or to check your work!

Q: Why do I get the same answer when I multiply the square roots differently?

The commutative property means $ \sqrt{81} \times \sqrt{4} = \sqrt{4} \times \sqrt{81} $. Order doesn't matter for multiplication!

Q: How do I know if 81, 4, and 9 are perfect squares?

Think: what number times itself gives this result? $ 9 \times 9 = 81 $, $ 2 \times 2 = 4 $, $ 3 \times 3 = 9 $. Practice recognizing these patterns!

Square Root Operations with Fraction Simplification

Solve the following exercise:

$\frac{\sqrt{81}\cdot\sqrt{4}}{\sqrt{9}\cdot\sqrt{9}}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's solve this problem together.

00:17 When you multiply the square root of number A, with the square root of number B.

00:22 You get the square root, of the product, A times B.

00:28 Now, let's use this formula, to work on our exercise, step by step.

00:36 Remember to simplify, wherever you can.

00:43 Great job! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{\sqrt{81}\cdot\sqrt{4}}{\sqrt{9}\cdot\sqrt{9}}=$

Step-by-step solution

To solve the problem, we'll simplify the expression $\frac{\sqrt{81}\cdot\sqrt{4}}{\sqrt{9}\cdot\sqrt{9}}$ using square root properties and arithmetic operations.

Step 1: Simplify each square root individually:

$\sqrt{81} = 9$ , $\sqrt{4} = 2$ .
Both $\sqrt{9}$ terms are equal to 3.

Thus, the expression becomes

\frac{9 \cdot 2}{3 \cdot 3}

Step 2: Perform multiplication of numbers:

Numerator: $9 \times 2 = 18$ .
Denominator: $3 \times 3 = 9$ .

The expression is now

\frac{18}{9}

Step 3: Simplify the fraction:

$\frac{18}{9} = 2$ , after dividing both the numerator and the denominator by the GCD, which is 9.

Therefore, the solution to the problem is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify square roots of perfect squares before multiplying or dividing
Technique: Calculate $\sqrt{81} = 9$ and $\sqrt{4} = 2$ first, giving $\frac{9 \times 2}{3 \times 3}$
Check: Verify final answer by calculating step by step: 18 ÷ 9 = 2 ✓

Common Mistakes

Avoid these frequent errors

Trying to simplify the entire expression under one square root
Don't combine terms like $\sqrt{81 \times 4} \div \sqrt{9 \times 9}$ = confused calculations! This makes the problem unnecessarily complex and leads to errors. Always simplify each individual square root first, then perform the arithmetic operations.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\sqrt{\frac{2}{4}}=$

FAQ

Everything you need to know about this question

Do I need to memorize all perfect squares?

Not all, but knowing common ones helps! Focus on perfect squares up to 144: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. These appear frequently in problems.

Can I use a calculator for square roots?

For perfect squares like $\sqrt{81}$ , try to recognize them mentally first. Calculators are helpful for non-perfect squares or to check your work!

Why do I get the same answer when I multiply the square roots differently?

The commutative property means $\sqrt{81} \times \sqrt{4} = \sqrt{4} \times \sqrt{81}$ . Order doesn't matter for multiplication!

What if the final fraction doesn't simplify to a whole number?

That's perfectly normal! Not all problems result in whole numbers. Just make sure your fraction is in simplest form by dividing by the greatest common divisor.

How do I know if 81, 4, and 9 are perfect squares?

Think: what number times itself gives this result? $9 \times 9 = 81$ , $2 \times 2 = 4$ , $3 \times 3 = 9$ . Practice recognizing these patterns!

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Solve: (√81 × √4)/(√9 × √9) - Square Root Fraction Simplification

Square Root Operations with Fraction Simplification

❤️ Continue Your Math Journey!

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

Do I need to memorize all perfect squares?

Can I use a calculator for square roots?

Why do I get the same answer when I multiply the square roots differently?

What if the final fraction doesn't simplify to a whole number?

How do I know if 81, 4, and 9 are perfect squares?

🌟 Unlock Your Math Potential

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