Simplification, Surds and Indices — Practice

Question 1

Simplify: 12 + 6 ÷ 2 × 3 − 4.
(a) 13 (b) 17 (c) 23 (d) 5

Accepted Answer

(b) 17.

Division and multiplication left to right: 6 ÷ 2 = 3, × 3 = 9; then 12 + 9 − 4 = 17.

Question 2

Find: 3/4 of 80 + 2/5 of 50.
(a) 70 (b) 75 (c) 80 (d) 85

Accepted Answer

(c) 80.

3/4 of 80 = 60, 2/5 of 50 = 20, sum = 80.

Question 3

Value of (2^5 × 2^3) ÷ 2^6 is:
(a) 2 (b) 4 (c) 8 (d) 16

Accepted Answer

(b) 4.

2^(5+3−6) = 2^2 = 4.

Question 4

The value of 16^(3/4) is:
(a) 6 (b) 8 (c) 12 (d) 64

Accepted Answer

(b) 8.

16 = 2⁴, so (2⁴)^(3/4) = 2³ = 8.

Question 5

Simplify 1/(√3 − √2).
(a) √3 − √2 (b) √3 + √2 (c) √6 (d) 1

Accepted Answer

(b) √3 + √2.

Multiply top and bottom by the conjugate √3 + √2: denominator becomes 3 − 2 = 1, leaving √3 + √2.

Question 6

If 3^(x+1) = 81, then x equals:
(a) 2 (b) 3 (c) 4 (d) 5

Accepted Answer

(b) 3.

81 = 3⁴, so equal bases give x + 1 = 4, x = 3.

Question 7

Evaluate (0.6³ + 0.4³) ÷ (0.6² − 0.6 × 0.4 + 0.4²).
(a) 0.2 (b) 0.5 (c) 1 (d) 1.2

Accepted Answer

(c) 1.

This is (a³+b³)/(a²−ab+b²) = a + b = 0.6 + 0.4 = 1.

Question 8

Simplify √(7 + 4√3).
(a) 2 + √3 (b) 1 + √3 (c) √3 + √4 (d) 2 + √5

Accepted Answer

(a) 2 + √3.

Write 7 + 4√3 = 7 + 2√12. Need x + y = 7 and xy = 12 → x = 4, y = 3. So √4 + √3 = 2 + √3. Check: (2+√3)² = 7 + 4√3 ✓.

Question 9

Simplify 2 + 1/(2 + 1/2).
(a) 12/5 (b) 5/2 (c) 9/4 (d) 7/3

Accepted Answer

(a) 12/5.

Inner: 2 + 1/2 = 5/2; its reciprocal is 2/5; total 2 + 2/5 = 12/5.

Question 10

The value of 39.99% of 1299 + 28.02% of 601 is approximately:
(a) 620 (b) 660 (c) 688 (d) 720

Accepted Answer

(c) 688.

Round: 40% of 1300 = 520, 28% of 600 = 168, sum ≈ 688.

Practice — Simplification, Surds and Indices