Q.1 Simplify: √50 + √18
7√2
8√2
5√2
6√2
Explanation - √50 = 5√2, √18 = 3√2. So, 5√2 + 3√2 = 8√2.
Correct answer is: 7√2
Q.2 Simplify: (3√2)²
6
9√2
18
12
Explanation - (3√2)² = 3² * (√2)² = 9 * 2 = 18
Correct answer is: 18
Q.3 If 2^x = 16, find x.
2
3
4
5
Explanation - 16 = 2^4, so 2^x = 2^4 ⇒ x = 4
Correct answer is: 4
Q.4 Simplify: √72 - √8
4√2
6√2
2√2
8√2
Explanation - √72 = 6√2, √8 = 2√2. Difference = 6√2 - 2√2 = 4√2
Correct answer is: 4√2
Q.5 If 3^(2x) = 81, find x.
1
2
3
4
Explanation - 81 = 3^4. So, 3^(2x) = 3^4 ⇒ 2x = 4 ⇒ x = 2
Correct answer is: 2
Q.6 Simplify: (√3 + √2)(√3 - √2)
1
5
-1
0
Explanation - Use (a+b)(a-b) = a² - b²: (√3)² - (√2)² = 3 - 2 = 1
Correct answer is: 1
Q.7 Find the value of 8^(2/3).
2
4
6
8
Explanation - 8^(2/3) = (2^3)^(2/3) = 2^(3*2/3) = 2^2 = 4
Correct answer is: 4
Q.8 Simplify: √32 × √2
8
4
16
32
Explanation - √32 × √2 = √(32*2) = √64 = 8
Correct answer is: 8
Q.9 If 5^(x-1) = 25, find x.
2
3
4
5
Explanation - 25 = 5^2. So, 5^(x-1) = 5^2 ⇒ x-1 = 2 ⇒ x = 3
Correct answer is: 3
Q.10 Simplify: √18 ÷ √2
3
√9
√6
√16
Explanation - √18 ÷ √2 = √(18/2) = √9 = 3
Correct answer is: 3
Q.11 Simplify: (2√5)^2
10
20
25
40
Explanation - (2√5)^2 = 2^2 * (√5)^2 = 4 * 5 = 20
Correct answer is: 20
Q.12 Find x if 9^(x+1) = 27
1/2
1/3
2/3
1
Explanation - 9 = 3^2, 27 = 3^3. So, (3^2)^(x+1) = 3^3 ⇒ 3^(2x+2) = 3^3 ⇒ 2x+2 =3 ⇒ x=1/2
Correct answer is: 1/2
Q.13 Simplify: √50 × √2
5
10
√100
7√2
Explanation - √50 × √2 = √(50*2) = √100 = 10
Correct answer is: 10
Q.14 If 2^(3x) = 32, find x.
1/3
5/3
2/3
None of these
Explanation - 32 = 2^5, so 2^(3x) = 2^5 ⇒ 3x = 5 ⇒ x = 5/3
Correct answer is: 5/3
Q.15 Simplify: (√7 + 2√3)^2
19 + 4√21
7 + 12√21
7 + 4√21
19 + 2√21
Explanation - (√7 + 2√3)^2 = (√7)^2 + 2*√7*2√3 + (2√3)^2 = 7 + 4√21 + 12 = 19 + 4√21
Correct answer is: 19 + 4√21
Q.16 Simplify: (27)^(2/3)
3
6
9
12
Explanation - 27 = 3^3, so 27^(2/3) = (3^3)^(2/3) = 3^(3*2/3) = 3^2 = 9
Correct answer is: 9
Q.17 Simplify: √8 + √18 - √2
4√2
5√2
6√2
3√2
Explanation - √8 = 2√2, √18 = 3√2, √2 = √2 ⇒ 2√2 + 3√2 - √2 = 4√2
Correct answer is: 5√2
Q.18 If 4^(x+1) = 64, find x.
2
3
4
5
Explanation - 64 = 4^3, so 4^(x+1) = 4^3 ⇒ x+1 =3 ⇒ x=2
Correct answer is: 2
Q.19 Simplify: (√6)^4
6
36
12
216
Explanation - (√6)^4 = (√6)^2 * (√6)^2 = 6*6 =36
Correct answer is: 36
Q.20 Simplify: 16^(3/4)
8
4
2
16
Explanation - 16 = 2^4 ⇒ 16^(3/4) = (2^4)^(3/4) = 2^(4*3/4) = 2^3 = 8
Correct answer is: 8
Q.21 Simplify: √45 ÷ √5
√5
3
9
5√5
Explanation - √45 ÷ √5 = √(45/5) = √9 = 3
Correct answer is: 3
Q.22 Simplify: (√2 + √3)(√2 - √3)
-1
1
5
-5
Explanation - Use (a+b)(a-b) = a^2 - b^2: 2 - 3 = -1
Correct answer is: -1
Q.23 If 8^(x-1) = 2, find x.
1
4/3
2/3
None of these
Explanation - 8 = 2^3, so 2^(3*(x-1)) = 2 ⇒ 3(x-1)=1 ⇒ x = 4/3
Correct answer is: 4/3
Q.24 Simplify: √27 + √12
5√3
6√3
7√3
8√3
Explanation - √27 = 3√3, √12 = 2√3 ⇒ sum = 5√3
Correct answer is: 5√3
Q.25 If 3^(x+2) = 81, find x.
1
2
3
0
Explanation - 81 = 3^4, so 3^(x+2) = 3^4 ⇒ x+2 =4 ⇒ x=2
Correct answer is: 0