If x, y are both positive rational numbers:

If x, y are both positive rational numbers, then (√x + √y) (√x – √y) is

(a) A rational number

(b) An irrational number

(c) Neither rational nor irrational number

(d) Both rational as well as irrational number

Solution:

(√x + √y) (√x – √y) = (√x)²– (√y)². x – y is a rational number option (c) is correct

After rationalizing the denominator of 7/3√3-2√2, we get the denominator as

(a) 13

(b) 19

(c) 5

(d) 35

Solution:

7/3√3-2√2 = 7/3√3-2√2 × 3√3+2√2/3√3+2√2 = 21√3+14√2/(3√3)²-(2√2)²

= 7(3√3+2√2)/17-8 = 7(3√3+2√2)/19  option (b) is correct

More Solutions:

• Express the following numbers in the form p/q.
• Classify the following numbers as rational or irrational:
• what can you say about the prime factors of q?
• Insert an irrational number between the following.
• Insert two irrational numbers between 2 and 3.
• Find one rational number between √2 and √3.
• Insert irrational numbers between √5 and √7.
• Simplify the following: (i) √45 – 3√20 + 4√5
• Simplify the following: (i) (5 + √7) (2 + √5).