Question

QUESTION-1

a) prove that ( 5 + √2) and (2√3 -7) are irrational number

b) locate √10 and √17 on the number line.

c) Insert two irrational number between √3 and √7

QUESTION -2

a) Rationalise the denominator 10

2√2+√3

b) state if the following fractions has a terminating decimal 59

75

.

147

160

give reason.

c)write ascending order 2√5, √3 and 5√2

d) find the value of a’ and b’

√3−1

√3+1

= a + b√3​

Answer 1

Answer:

Q,1a, Let’s assume on the contrary that 5 – 2√3 is a rational number. Then, there exist co prime positive integers a and b such that 5 – 2√3 = abab ⇒ 2√3 = 5 – abab ⇒ √2 = (5b–a)(2b)(5b–a)(2b) ⇒ √2 is rational [∵ 2, a and b are integers ∴ (5b–a)(2b)(5b–a)(2b) is a rational number] This contradicts the fact that √2 is irrational. So, our assumption is incorrect. Hence, 5 – 2√3 is an irrational number.Read more on Sarthaks.com - https://www.sarthaks.com/623048/show-that-5-23-is-an-irrational-number.