Solve: (√4 × √9)/√16 - Square Root Multiplication and Division

Square Root Operations with Perfect Squares

Solve the following exercise:

4⋅916= \frac{\sqrt{4}\cdot\sqrt{9}}{\sqrt{16}}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's solve this problem together.
00:12 When multiplying the square root of A with the square root of B,
00:16 the answer is the square root of A times B.
00:20 Let's use this idea to solve our exercise. First, calculate the product.
00:32 When you square the square root of any number, it removes the square root.
00:40 Apply this to our exercise, and let's clear out the squares.
00:50 Break 6 into its factors: three and two.
00:54 Break 4 into its factors: two and two.
00:59 And there you have it. That's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

4⋅916= \frac{\sqrt{4}\cdot\sqrt{9}}{\sqrt{16}}=

2

Step-by-step solution

To solve this problem, let's carefully follow these steps:

  • Step 1: Simplify each square root:

4=2,9=3,16=4 \sqrt{4} = 2, \quad \sqrt{9} = 3, \quad \sqrt{16} = 4

  • Step 2: Calculate the expression in the numerator:

The expression in the numerator is 4⋅9\sqrt{4} \cdot \sqrt{9}. Substituting the simplified values, we have:
2⋅3=62 \cdot 3 = 6

  • Step 3: Compute the division with the denominator:

Now, divide the result from Step 2 by the simplified denominator:
64=32 \frac{6}{4} = \frac{3}{2}

Thus, the value of the expression is 32\frac{3}{2}.

Therefore, the solution to the problem is 32\frac{3}{2}.

3

Final Answer

32 \frac{3}{2}

Key Points to Remember

Essential concepts to master this topic
  • Perfect Squares: Recognize that 4, 9, and 16 are perfect squares
  • Simplification: Calculate 4=2 \sqrt{4} = 2 , 9=3 \sqrt{9} = 3 , 16=4 \sqrt{16} = 4 first
  • Check: Verify by substituting: 2⋅34=64=32 \frac{2 \cdot 3}{4} = \frac{6}{4} = \frac{3}{2} ✓

Common Mistakes

Avoid these frequent errors
  • Trying to simplify the entire expression before finding individual square roots
    Don't try to combine square roots first like 4⋅9÷16 \sqrt{4 \cdot 9} ÷ \sqrt{16} = wrong approach! This makes the problem unnecessarily complex and leads to errors. Always simplify each square root individually first, then perform the arithmetic operations.

Practice Quiz

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FAQ

Everything you need to know about this question

Do I need to memorize perfect squares?

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Yes! Memorizing perfect squares like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 will make square root problems much faster. These appear frequently in math problems.

Can I use a calculator for square roots?

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While calculators help, it's important to recognize perfect squares by sight. This builds number sense and makes you faster at mental math!

What if the final answer isn't a whole number?

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That's completely normal! In this problem, 32 \frac{3}{2} is the correct answer. Always simplify fractions to their lowest terms.

Why do I get the wrong answer when I don't simplify square roots first?

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Square roots of perfect squares give you exact whole numbers. If you don't simplify them first, you'll be working with messy decimals or complicated expressions that lead to calculation errors.

Should I convert fractions to decimals?

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Keep fractions as fractions! 32 \frac{3}{2} is more precise than 1.5, and many math teachers prefer exact fractional answers over decimal approximations.

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