Rational and Irrational Numbers Quiz

Find the value of the given rational number with a rational denominator.

1. (3√3 + √3)(√8 + √2)/30
2. ((√27 + √3) + (√8 + √2))/30
3. (3√3 + √3)(√8 + √2)/40
4. ((√27 + √3) + (√8 + √2))/40

Answer: (b) ((√27 + √3) + (√8 + √2))/30

If 0 < y < x, which of the option statement must be true?

1. √x - √y = √(x - y)
2. x + √x + y + √y = 2√x + y
3. √(xy) = √x √y
4. x√y = y√x

Answer: (c) √(xy) = √x √y

Which of the option must be placed in the middle (3rd) if the given options are to be arranged in decreasing order?

1. 2/(1/√11 + 1/√13)
2. √12
3. (√11 + √13)/2
4. π

Answer: (a) 2/(1/√11 + 1/√13)

What is the value of q + r - p in the given expression, If the p < r < q.

1. 245
2. 361
3. 360
4. 300

Answer: (b) 361

If x = 1/(7 + 4√3), y = 1/(7 - 4√3), find the value of 5x2 - 7xy - 5y2.

1. 5 + 80√3
2. - 7 (1 - 80√3)
3. -7 - 560√3
4. 7 + 80√3

Answer: (c) -7 - 560√3

Find the value of the given expression.

1. 3
2. 0
3. 2
4. 1

Answer: (c) 2

What is the value of the given expression?

1. √2
2. 2√2
3. 0
4. 1

Answer: (d) 1

If a = (√5 + √3)/2 , then what is the value of a4 + 1/a4?

1. 9
2. 7
3. 4
4. 8

Answer: (b) 7

If x = 7 + 4√3 and xy = 1, then find the value of 1/x2 + 1/y2

1. 115
2. 185
3. 230
4. 194

Answer: (d) 194

Find the value of the given expression.

1. 2√10
2. -2√2
3. 1
4. 0

Answer: (a) 2√10