a³ = a × a × a
∛a = a¹/³
∛(a × b) = ∛a × ∛b
∛(a/b) = ∛a/∛b
a³/b³ = (a/b)³
∛a³ = a
(a³)¹/³ = a
∛(a³ × b³) = a × b
∛(a³ ÷ b³) = a ÷ b

🪤 The 5 Mistakes That Cost Marks

Not simplifying cube roots of perfect cubes
Not using the formula ∛(a × b) = ∛a × ∛b
Not using the formula ∛(a/b) = ∛a/∛b
Not simplifying expressions with cube roots
Not checking the units of the answer

✏️ 3 Solved PYQs

Question 1: Find the cube root of 125 Step 1: We know that 5³ = 125 Step 2: So, ∛125 = ∛(5³) Step 3: Using the formula ∛(a³) = a get ∛125 = 5
Question 2: Find the cube root of 216 Step 1: We know that 6³ = 216 Step 2: So, ∛216 = ∛(6³) Step 3: Using the formula ∛(a³) = a get ∛216 = 6
Question 3: Find the cube root of 8 Step 1: We know that 2³ = 8 Step 2: So, ∛8 = ∛(2³) Step 3: Using the formula ∛(a³) = a get ∛8 = 2

🧠 The One Thing Most Students Get Wrong

Most students get confused between cube and cube root, they think that ∛a = a³ which is incorrect, ∛an is the number that when multiplied by itself three times gives a for example ∛8 = 2 because 2 × 2 × 2 = 8

👁️ Ayush's Note

To find the cube root of a number, try to find the number that when multiplied by itself three times gives the original number
Use the formula ∛(a × b) = ∛a × ∛b to simplify expressions with cube roots
Use the formula ∛(a/b) = ∛a/∛b to simplify expressions with cube roots

🔁 Last 5 Minutes Box

Make sure to simplify all expressions with cube roots
Check the units of the answer
Use the formula ∛(a³) = a to simplify expressions with cube roots
Use the formula ∛(a × b) = ∛a × ∛b to simplify expressions with cube roots
Use the formula ∛(a/b) = ∛a/∛b to simplify expressions with cube roots

📝 Practice MCQs

1. What is the cube root of 27?

A) 2

B) 3

C) 4

D) 5

Answer: B) 3 because 3 × 3 × 3 = 27

2. What is the cube root of 64?

A) 2

B) 3

C) 4

D) 5

Answer: C) 4 because 4 × 4 × 4 = 64

3. What is the cube root of 1?

A) 0

B) 1

C) 2

D) 3

Answer: B) 1 because 1 × 1 × 1 = 1

4. What is the cube root of 125?

A) 4

B) 5

C) 6

D) 7

Answer: B) 5 because 5 × 5 × 5 = 125

5. What is the cube root of 8?

A) 1

B) 2

C) 3

D) 4

Answer: B) 2 because 2 × 2 × 2 = 8

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

a³ = a × a × a
∛a = a¹/³
∛(a × b) = ∛a × ∛b
∛(a/b) = ∛a/∛b
a³/b³ = (a/b)³
∛a³ = a
(a³)¹/³ = a
∛(a³ × b³) = a × b
∛(a³ ÷ b³) = a ÷ b

🪤 The 5 Mistakes That Cost Marks

Not simplifying cube roots of perfect cubes
Not using the formula ∛(a × b) = ∛a × ∛b
Not using the formula ∛(a/b) = ∛a/∛b
Not simplifying expressions with cube roots
Not checking the units of the answer

✏️ 3 Solved PYQs

Question 1: Find the cube root of 125 Step 1: We know that 5³ = 125 Step 2: So, ∛125 = ∛(5³) Step 3: Using the formula ∛(a³) = a get ∛125 = 5
Question 2: Find the cube root of 216 Step 1: We know that 6³ = 216 Step 2: So, ∛216 = ∛(6³) Step 3: Using the formula ∛(a³) = a get ∛216 = 6
Question 3: Find the cube root of 8 Step 1: We know that 2³ = 8 Step 2: So, ∛8 = ∛(2³) Step 3: Using the formula ∛(a³) = a get ∛8 = 2

🧠 The One Thing Most Students Get Wrong

Most students get confused between cube and cube root, they think that ∛a = a³ which is incorrect, ∛an is the number that when multiplied by itself three times gives a for example ∛8 = 2 because 2 × 2 × 2 = 8

👁️ Ayush's Note

To find the cube root of a number, try to find the number that when multiplied by itself three times gives the original number
Use the formula ∛(a × b) = ∛a × ∛b to simplify expressions with cube roots
Use the formula ∛(a/b) = ∛a/∛b to simplify expressions with cube roots

🔁 Last 5 Minutes Box

Make sure to simplify all expressions with cube roots
Check the units of the answer
Use the formula ∛(a³) = a to simplify expressions with cube roots
Use the formula ∛(a × b) = ∛a × ∛b to simplify expressions with cube roots
Use the formula ∛(a/b) = ∛a/∛b to simplify expressions with cube roots

📝 Practice MCQs

1. What is the cube root of 27?

A) 2

B) 3

C) 4

D) 5

Answer: B) 3 because 3 × 3 × 3 = 27

2. What is the cube root of 64?

A) 2

B) 3

C) 4

D) 5

Answer: C) 4 because 4 × 4 × 4 = 64

3. What is the cube root of 1?

A) 0

B) 1

C) 2

D) 3

Answer: B) 1 because 1 × 1 × 1 = 1

4. What is the cube root of 125?

A) 4

B) 5

C) 6

D) 7

Answer: B) 5 because 5 × 5 × 5 = 125

5. What is the cube root of 8?

A) 1

B) 2

C) 3

D) 4

Answer: B) 2 because 2 × 2 × 2 = 8

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides: