Q.1 Simplify: √50 × √8
√400
20
10√2
40
Explanation - √50 × √8 = √(50×8) = √400 = 20.
Correct answer is: 20
Q.2 Find the value of (√3 + 1)²
4 + 2√3
3 + 2√3
2 + √3
5 + √3
Explanation - (√3 + 1)² = 3 + 1 + 2√3 = 4 + 2√3.
Correct answer is: 4 + 2√3
Q.3 Simplify: (3√2) × (2√3)
6√6
5√5
3√6
2√2
Explanation - (3√2)(2√3) = 6√6.
Correct answer is: 6√6
Q.4 Simplify: (5√3)²
15
25√3
75
50
Explanation - (5√3)² = 25×3 = 75.
Correct answer is: 75
Q.5 If 5^(x) = 125, find x.
2
3
4
5
Explanation - 125 = 5³, so x = 3.
Correct answer is: 3
Q.6 Simplify: √(9/16)
3/4
4/3
9/16
16/9
Explanation - √(9/16) = √9 / √16 = 3/4.
Correct answer is: 3/4
Q.7 Simplify: (√5 + √2)(√5 - √2)
3
7
√3
5
Explanation - Using (a+b)(a−b) = a²−b² ⇒ (√5)²−(√2)² = 5−2 = 3.
Correct answer is: 3
Q.8 Simplify: (2 + √3)(2 - √3)
1
4
7
3
Explanation - (2+√3)(2−√3)=4−3=1.
Correct answer is: 1
Q.9 Simplify: (3 + 2√2)²
17 + 12√2
13 + 8√2
10 + 6√2
9 + 4√2
Explanation - (3 + 2√2)² = 9 + 8√2 + 8 = 17 + 12√2.
Correct answer is: 17 + 12√2
Q.10 Find the value of √(49/81)
7/9
9/7
1
3/7
Explanation - √(49/81)=7/9.
Correct answer is: 7/9
Q.11 If 2^(x+1)=16, find x.
2
3
4
5
Explanation - 16=2⁴, so x+1=4⇒x=3.
Correct answer is: 3
Q.12 Simplify: √32 + √8
8√2
6√2
4√2
10√2
Explanation - √32=4√2, √8=2√2 ⇒ sum = 6√2.
Correct answer is: 6√2
Q.13 Simplify: (2√3)³
8√3
12√3
24√3
24√9
Explanation - (2√3)³=8×3√3=24√3.
Correct answer is: 24√3
Q.14 Find x if 3^(2x) = 81.
2
3
4
5
Explanation - 81=3⁴ ⇒ 2x=4 ⇒ x=2.
Correct answer is: 2
Q.15 Simplify: (√7 - 1)²
8 - 2√7
7 - 2√7 + 1
6 - 2√7
7 + 1 - √7
Explanation - (√7 - 1)² = 7 + 1 - 2√7 = 8 - 2√7.
Correct answer is: 8 - 2√7
Q.16 Simplify: 3√18 + 2√8
15√2
5√2
13√2
17√2
Explanation - √18=3√2 ⇒3×3√2=9√2, √8=2√2 ⇒2×2√2=4√2 ⇒total=13√2.
Correct answer is: 13√2
Q.17 Simplify: (4√5)/(2√5)
1
2
3
4
Explanation - (4√5)/(2√5)=4/2=2.
Correct answer is: 2
Q.18 Simplify: (√3/√12)
1/2
√4
2
1/√4
Explanation - √3/√12=√(3/12)=√(1/4)=1/2.
Correct answer is: 1/2
Q.19 Simplify: 5^(3) × 5^(2)
5⁵
5⁶
5⁷
5⁸
Explanation - When bases same, add powers: 3+2=5 ⇒ 5⁵.
Correct answer is: 5⁵
Q.20 Simplify: (√2 + 1)(√2 - 1)
1
2
3
√2
Explanation - (√2+1)(√2−1)=2−1=1.
Correct answer is: 1
Q.21 Find x: 2^(x-1)=8
2
3
4
5
Explanation - 8=2³ ⇒ x−1=3 ⇒ x=4.
Correct answer is: 4
Q.22 Simplify: (27)^(1/3)
3
9
6
4
Explanation - Cube root of 27 is 3.
Correct answer is: 3
Q.23 Simplify: (16)^(3/4)
8
16
4√4
2
Explanation - 16^(1/4)=2 ⇒ (2)³=8.
Correct answer is: 8
Q.24 Simplify: (9)^(1/2) × (9)^(1/2)
9
3
6
1
Explanation - (9)^(1/2)×(9)^(1/2)=(9)^(1)=9.
Correct answer is: 9
Q.25 Simplify: (64)^(1/6) × (64)^(1/3)
8
4
2
16
Explanation - Add powers: 1/6+1/3=1/2 ⇒ 64^(1/2)=8, correction: √64=8. (64^(1/6+1/3)=64^(1/2)=8). Correct is 8.
Correct answer is: 4