Question 1

If √(x) = 5, find the value of x^(3/2).

Accepted Answer

Step 1: From √x = 5, we get x = 25. Step 2: Compute x^(3/2) = (x^(1/2))³ = (√x)³ = 5³ = 125.

Question 2

Simplify: 48 ÷ 6 + 12 × 2 − 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 48 ÷ 6 = 8 and 12 × 2 = 24. Step 2: Now we have 8 + 24 − 5. Step 3: Addition and Subtraction (left to right): 8 + 24 = 32, then 32 − 5 = 27.

Question 3

Simplify: 2 + 8 × 3 − 12 ÷ 2

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 8 × 3 = 24 and 12 ÷ 2 = 6. Step 2: Now we have 2 + 24 − 6. Step 3: Addition and Subtraction (left to right): 2 + 24 = 26, then 26 − 6 = 20.

Question 4

Calculate: 60 ÷ 3 × 2 + 10 − 4

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 60 ÷ 3 = 20, then 20 × 2 = 40. Step 2: Now we have 40 + 10 − 4. Step 3: Addition and Subtraction (left to right): 40 + 10 = 50, then 50 − 4 = 46.

Question 5

Evaluate: 36 ÷ 6 + 7 × 3 − 9

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 36 ÷ 6 = 6 and 7 × 3 = 21. Step 2: Now we have 6 + 21 − 9. Step 3: Addition and Subtraction (left to right): 6 + 21 = 27, then 27 − 9 = 18.

Question 6

Simplify: ∛(27) × ∜(16) ÷ √(4)

Accepted Answer

Step 1: ∛(27) = ∛(3³) = 3. Step 2: ∜(16) = ∜(2⁴) = 2. Step 3: √(4) = 2. Step 4: Compute: 3 × 2 ÷ 2 = 3.

Question 7

Solve: 5 × 4 + 6 ÷ 2 − 8

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first. 5 × 4 = 20 and 6 ÷ 2 = 3. Step 2: Now we have 20 + 3 − 8. Step 3: Addition and Subtraction (left to right): 20 + 3 = 23, then 23 − 8 = 15.

Question 8

Evaluate: 100 − 20 ÷ 4 + 3 × 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 20 ÷ 4 = 5 and 3 × 5 = 15. Step 2: Now we have 100 − 5 + 15. Step 3: Subtraction and Addition (left to right): 100 − 5 = 95, then 95 + 15 = 110.

Question 9

Simplify: 2 + 6 × 4 ÷ 2 − 3 + 5

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 6 × 4 = 24, then 24 ÷ 2 = 12. Step 2: Rewrite as 2 + 12 − 3 + 5. Step 3: Addition and Subtraction (left to right): 2 + 12 = 14, 14 − 3 = 11, 11 + 5 = 16. Therefore, answer is 16.

Question 10

Calculate: 48 ÷ 6 × 2 + 10 − 4 × 3

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 48 ÷ 6 = 8, then 8 × 2 = 16. Also, 4 × 3 = 12. Step 2: Rewrite as 16 + 10 − 12. Step 3: Addition and Subtraction (left to right): 16 + 10 = 26, 26 − 12 = 14. Therefore, answer is 14.

Question 11

Simplify: 144 ÷ 12 + 8 × 3 − 5 + 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 144 ÷ 12 = 12 and 8 × 3 = 24. Step 2: Rewrite as 12 + 24 − 5 + 2. Step 3: Addition and Subtraction (left to right): 12 + 24 = 36, 36 − 5 = 31, 31 + 2 = 33. Therefore, answer is 33.

Question 12

Evaluate: 100 − 20 × 3 + 15 ÷ 3 − 10

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 20 × 3 = 60 and 15 ÷ 3 = 5. Step 2: Rewrite as 100 − 60 + 5 − 10. Step 3: Subtraction and Addition (left to right): 100 − 60 = 40, 40 + 5 = 45, 45 − 10 = 35. Therefore, answer is 35.

Question 13

Solve: 72 ÷ 8 + 5 × 3 − 2 × 4 + 1

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 72 ÷ 8 = 9, 5 × 3 = 15, and 2 × 4 = 8. Step 2: Rewrite as 9 + 15 − 8 + 1. Step 3: Addition and Subtraction (left to right): 9 + 15 = 24, 24 − 8 = 16, 16 + 1 = 17. Therefore, answer is 17.

Question 14

What is the value of 5 + 3 × 4 − 8 ÷ 2 + 6?

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 3 × 4 = 12 and 8 ÷ 2 = 4. Step 2: Rewrite as 5 + 12 − 4 + 6. Step 3: Addition and Subtraction (left to right): 5 + 12 = 17, 17 − 4 = 13, 13 + 6 = 19. Therefore, answer is 19.

Question 15

Simplify: (√5 + √3)^2 / (√5 - √3) × (√5 + √3) / (√5 + √3)^2. What is the result?

Accepted Answer

Step 1: Simplify the denominator (√5 - √3)(√5 + √3) = 5 - 3 = 2. Step 2: Cancel (√5 + √3)^2 from numerator and denominator: [(√5 + √3)^2 × (√5 + √3)] / [2 × (√5 + √3)^2] = (√5 + √3) / 2. Step 3: Rationalize: (√5 + √3) / 2 ≈ (2.236 + 1.732) / 2 ≈ 1.984 ≈ 2 (exact form is (√5 + √3)/2).

Question 16

Simplify: 144 ÷ 12 + 8 × 3 − 5 + 2 × (15 − 9)

Accepted Answer

Step 1: Solve brackets first: (15 − 9) = 6. Step 2: Perform division and multiplication left to right: 144 ÷ 12 = 12 and 8 × 3 = 24 and 2 × 6 = 12. Step 3: Now we have: 12 + 24 − 5 + 12. Step 4: Perform addition and subtraction left to right: 12 + 24 = 36, then 36 − 5 = 31, then 31 + 12 = 43. Therefore, the answer is 43.

Question 17

Evaluate: 256 ÷ 16 × 2 + 18 − 3 × 4 ÷ 2

Accepted Answer

Step 1: Perform division and multiplication from left to right: 256 ÷ 16 = 16, then 16 × 2 = 32. Step 2: For the second part: 3 × 4 = 12, then 12 ÷ 2 = 6. Step 3: Now we have: 32 + 18 − 6. Step 4: Perform addition and subtraction left to right: 32 + 18 = 50, then 50 − 6 = 44. Therefore, the answer is 44.

Question 18

Simplify: 7 + 8 ÷ 4 × 6 − 3 + 12 ÷ 3 × 2

Accepted Answer

Step 1: Identify and perform all division and multiplication from left to right: 8 ÷ 4 = 2, then 2 × 6 = 12. Also: 12 ÷ 3 = 4, then 4 × 2 = 8. Step 2: Rewrite the expression: 7 + 12 − 3 + 8. Step 3: Perform addition and subtraction from left to right: 7 + 12 = 19, then 19 − 3 = 16, then 16 + 8 = 24. Therefore, the answer is 24.

Question 19

Calculate: 100 − 50 ÷ 5 + 3 × 8 − 12 ÷ 4 × 2

Accepted Answer

Step 1: Perform all division and multiplication from left to right: 50 ÷ 5 = 10, 3 × 8 = 24, 12 ÷ 4 = 3, then 3 × 2 = 6. Step 2: Rewrite: 100 − 10 + 24 − 6. Step 3: Perform addition and subtraction from left to right: 100 − 10 = 90, then 90 + 24 = 114, then 114 − 6 = 108. Therefore, the answer is 108.

Question 20

If 3^(2x - 1) × 9^(x + 1) = 27^(x/3), find the value of x.

Accepted Answer

Step 1: Express all terms with base 3: 3^(2x - 1) × (3^2)^(x + 1) = (3^3)^(x/3). Step 2: Simplify: 3^(2x - 1) × 3^(2x + 2) = 3^x. Step 3: Combine left side: 3^(2x - 1 + 2x + 2) = 3^x → 3^(4x + 1) = 3^x. Step 4: Equate exponents: 4x + 1 = x → 3x = -1 → x = -1/3.

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