Question

ii) Show that 3+√5 is an irrational number iii) Compare the pair of surds 7 √2, 5√3 iv) Rationalize the denominator. 1 √7+√2​

Answer 1

Answer:

ii) Let us assume that 3 + √5 is a rational number. ... So, {(a - 3b)/b} should also be an irrational number. Hence, it is a contradiction to our assumption. Thus, 3 + √5 is an irrational number.

iii) In order to compare the two swords 7 root 2 and 5 root 3 . we have to square these two surds.By squaring we get 98 and 75 respectively. 98 is Greater . so 7 root 2 is Greater than 5 root 3.

iv) √7+2/ 3 is the answer

Answer 2

Step-by-step explanation:

Since, 5=20×51

⇒ The denominator is in the form of 2m×5n, where m and n are non-negative integers.

So, the decimal form of

13

5

will be terminating type.

(ii)

2

11

Since, 11=20×50×111

⇒ The denominator is not in the form of 2m×5n, where m and n are non-negative integers.

So, the decimal form of

2

11

will be non-terminating recurring type.

(iii)

29

16

Since, 16=24×50

⇒ The denominator is in the form of 2m×5n, where m and n are non-negative integers.

So, the decimal form of

29

16