a² - b² = (a + b)(a - b)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
√(a²) = a
(√a)² = a
√(ab) = √a × √b
√(a/b) = √a / √b
(√a)ⁿ = aⁿ⁄²
a² = (a) × (a)
√a × √a = a

🪤 The 5 Mistakes That Cost Marks

Not simplifying the expression before finding the square root
Not using the formula (a + b)² = a² + 2ab + b² to simplify expressions
Not using the formula a² - b² = (a + b)(a - b) to factorize expressions
Not using the formula (√a)² = a to simplify square root expressions
Not using the formula √(ab) = √a × √b to simplify square root expressions

✏️ 3 Solved PYQs

Question 1: Simplify (√5)² Step 1: Use the formula (√a)² = a Step 2: Substitute a = 5 into the formula Step 3: Simplify the expression to get the answer Answer: 5
Question 2: Find the value of an if (a + 3)² = 64 Step 1: Use the formula (a + b)² = a² + 2ab + b² Step 2: Substitute b = 3 and the given value into the formula Step 3: Simplify the expression to get a² + 6a + 9 = 64 Step 4: Rearrange the equation to get a² + 6a - 55 = 0 Step 5: Factorize the equation to get (a + 11)(a - 5) = 0 Step 6: Solve for a to get a = -11 or a = 5
Question 3: Simplify √(16/9) Step 1: Use the formula √(a/b) = √a / √b Step 2: Substitute a = 16 and b = 9 into the formula Step 3: Simplify the expression to get √16 / √9 Step 4: Simplify the square roots to get 4/3

🧠 The One Thing Most Students Get Wrong

Most students get wrong the simplification of expressions involving square roots and the use of formulas to simplify expressions
They often forget to use the formulas (a + b)² = a² + 2ab + b² and a² - b² = (a + b)(a - b) to simplify expressions
They also often forget to use the formulas (√a)² = a and √(ab) = √a × √b to simplify square root expressions

👁️ Ayush's Note

To excel ∈ squares and square roots, practice simplifying expressions using the formulas
Make sure to use the formulas (a + b)² = a² + 2ab + b² and a² - b² = (a + b)(a - b) to simplify expressions
Also, use the formulas (√a)² = a and √(ab) = √a × √b to simplify square root expressions
Practice solving questions involving squares and square roots to build confidence and speed

🔁 Last 5 Minutes Box

Go through the formulas one last time
Make sure to remember the formulas (a + b)² = a² + 2ab + b² and a² - b² = (a + b)(a - b)
Also, remember the formulas (√a)² = a and √(ab) = √a × √b
Take a few deep breaths and stay calm
Read each question carefully and choose the correct answer

📝 Practice MCQs

1. What is the value of (√9)²?

A) 3

B) 9

C) 12

D) 15

Answer: B) 9, using the formula (√a)² = a

2. What is the value of (2 + 3)²?

A) 20

B) 25

C) 30

D) 35

Answer: B) 25, using the formula (a + b)² = a² + 2ab + b²

3. What is the value of √(16/4)?

A) 1

B) 2

C) 3

D) 4

Answer: B) 2, using the formula √(a/b) = √a / √b

4. What is the value of (5 - 2)²?

A) 9

B) 12

C) 15

D) 18

Answer: A) 9, using the formula (a - b)² = a² - 2ab + b²

5. What is the value of (√4) × (√9)?

A) 5

B) 6

C) 12

D) 15

Answer: B) 6, using the formula √(ab) = √a × √b

🚀 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.

📚 Academic References

Content verified against peer-reviewed research:

�Let the People Rap�: Cultural Rhetorics Pedagogy and Practices U... — Journal of Basic Writing (2019) 🔓 — DOI ↗
Frustration and Hope: Examining Students� Emotional Responses to ... — Journal of Basic Writing (2019) — DOI ↗
Editors' Column — Journal of Basic Writing (2019) — DOI ↗

🔓 = Open Access article

🎬 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:

a² - b² = (a + b)(a - b)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
√(a²) = a
(√a)² = a
√(ab) = √a × √b
√(a/b) = √a / √b
(√a)ⁿ = aⁿ⁄²
a² = (a) × (a)
√a × √a = a

🪤 The 5 Mistakes That Cost Marks

Not simplifying the expression before finding the square root
Not using the formula (a + b)² = a² + 2ab + b² to simplify expressions
Not using the formula a² - b² = (a + b)(a - b) to factorize expressions
Not using the formula (√a)² = a to simplify square root expressions
Not using the formula √(ab) = √a × √b to simplify square root expressions

✏️ 3 Solved PYQs

Question 1: Simplify (√5)² Step 1: Use the formula (√a)² = a Step 2: Substitute a = 5 into the formula Step 3: Simplify the expression to get the answer Answer: 5
Question 2: Find the value of an if (a + 3)² = 64 Step 1: Use the formula (a + b)² = a² + 2ab + b² Step 2: Substitute b = 3 and the given value into the formula Step 3: Simplify the expression to get a² + 6a + 9 = 64 Step 4: Rearrange the equation to get a² + 6a - 55 = 0 Step 5: Factorize the equation to get (a + 11)(a - 5) = 0 Step 6: Solve for a to get a = -11 or a = 5
Question 3: Simplify √(16/9) Step 1: Use the formula √(a/b) = √a / √b Step 2: Substitute a = 16 and b = 9 into the formula Step 3: Simplify the expression to get √16 / √9 Step 4: Simplify the square roots to get 4/3

🧠 The One Thing Most Students Get Wrong

Most students get wrong the simplification of expressions involving square roots and the use of formulas to simplify expressions
They often forget to use the formulas (a + b)² = a² + 2ab + b² and a² - b² = (a + b)(a - b) to simplify expressions
They also often forget to use the formulas (√a)² = a and √(ab) = √a × √b to simplify square root expressions

👁️ Ayush's Note

To excel ∈ squares and square roots, practice simplifying expressions using the formulas
Make sure to use the formulas (a + b)² = a² + 2ab + b² and a² - b² = (a + b)(a - b) to simplify expressions
Also, use the formulas (√a)² = a and √(ab) = √a × √b to simplify square root expressions
Practice solving questions involving squares and square roots to build confidence and speed

🔁 Last 5 Minutes Box

Go through the formulas one last time
Make sure to remember the formulas (a + b)² = a² + 2ab + b² and a² - b² = (a + b)(a - b)
Also, remember the formulas (√a)² = a and √(ab) = √a × √b
Take a few deep breaths and stay calm
Read each question carefully and choose the correct answer

📝 Practice MCQs

1. What is the value of (√9)²?

A) 3

B) 9

C) 12

D) 15

Answer: B) 9, using the formula (√a)² = a

2. What is the value of (2 + 3)²?

A) 20

B) 25

C) 30

D) 35

Answer: B) 25, using the formula (a + b)² = a² + 2ab + b²

3. What is the value of √(16/4)?

A) 1

B) 2

C) 3

D) 4

Answer: B) 2, using the formula √(a/b) = √a / √b

4. What is the value of (5 - 2)²?

A) 9

B) 12

C) 15

D) 18

Answer: A) 9, using the formula (a - b)² = a² - 2ab + b²

5. What is the value of (√4) × (√9)?

A) 5

B) 6

C) 12

D) 15

Answer: B) 6, using the formula √(ab) = √a × √b

🚀 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.

📚 Academic References

Content verified against peer-reviewed research:

�Let the People Rap�: Cultural Rhetorics Pedagogy and Practices U... — Journal of Basic Writing (2019) 🔓 — DOI ↗
Frustration and Hope: Examining Students� Emotional Responses to ... — Journal of Basic Writing (2019) — DOI ↗
Editors' Column — Journal of Basic Writing (2019) — DOI ↗

🔓 = Open Access article

🎬 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: