Solve for the Cube Root: Finding the Number in ☐³ = 5×5×5

Q: What's the difference between ☐² and ☐³?

☐² means multiply the number by itself once: 5² = 5×5 = 25☐³ means multiply the number by itself twice: 5³ = 5×5×5 = 125

Q: How do I find cube roots without a calculator?

Look for perfect cubes you know: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 6³=216. If you see 125, you know the cube root is 5!

Q: Why is the answer 5 and not something else?

Because 5×5×5 = 5³. The expression on the right shows 5 multiplied by itself three times, which is exactly what 5³ means!

Q: Can the answer be a decimal or fraction?

In this problem, no! Since 5×5×5 = 125 is a perfect cube, the answer must be a whole number. For non-perfect cubes, you might get decimals.

Cube Roots with Perfect Cube Recognition

Fill in the missing number:

$☐^3=5\cdot5\cdot5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing number

00:03 We will use the power formula

00:06 Any number (X) to the power of (N)

00:09 equals X multiplied by itself N times

00:18 We will use this formula in our exercise

00:22 X is the number being multiplied

00:28 We'll count the number of multiplications to find the unknown N

00:36 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

Fill in the missing number:

$☐^3=5\cdot5\cdot5$

Step-by-step solution

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

Step 1: Evaluate the power expression $5 \cdot 5 \cdot 5$
Step 2: Determine the number whose cube matches this evaluated expression
Step 3: Conclude with the missing number that satisfies $☐^3 = 5 \cdot 5 \cdot 5$

Now, let's work through these steps:

Step 1: Calculate the power expression.

$5 \cdot 5 \cdot 5 = 125$

Step 2: Determine the cube root of 125 to find the missing number.

Since $5^3 = 125$ , it follows that the missing number must be 5.

Step 3: Verify that $5^3 = 125$ .

Therefore, the solution to the given problem is $5$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Cube Rule: If $a^3 = b$ , then a is the cube root of b
Technique: Recognize $5 \cdot 5 \cdot 5 = 5^3 = 125$ pattern
Check: Verify $5^3 = 5 \times 5 \times 5 = 125$ ✓

Common Mistakes

Avoid these frequent errors

Confusing cube root with square root
Don't think ☐³ = 5×5×5 means ☐ = √125 ≈ 11.18! This confuses cubing with squaring. Always remember: if ☐³ equals something, then ☐ is the cube root, not the square root.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

What's the difference between ☐² and ☐³?

☐² means multiply the number by itself once: 5² = 5×5 = 25
☐³ means multiply the number by itself twice: 5³ = 5×5×5 = 125

How do I find cube roots without a calculator?

Look for perfect cubes you know: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 6³=216. If you see 125, you know the cube root is 5!

Why is the answer 5 and not something else?

Because 5×5×5 = 5³. The expression on the right shows 5 multiplied by itself three times, which is exactly what 5³ means!

What if I can't recognize the perfect cube?

Try small numbers systematically: Does 2³ work? 2×2×2 = 8 (no). Does 3³ work? 3×3×3 = 27 (no). Does 4³ work? 4×4×4 = 64 (no). Does 5³ work? 5×5×5 = 125 (yes!)

Can the answer be a decimal or fraction?

In this problem, no! Since 5×5×5 = 125 is a perfect cube, the answer must be a whole number. For non-perfect cubes, you might get decimals.

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