NUMBER SYSTEM CLASS 9 DPP
MATHEMATICS – IX
1) If a = 2 + √3 , then find the value of a-1/a
2) 6/(3√2-2√3)=3√2-a√3 , find the value of a?
3) In each of the following determine rational numbers a and b:
(i) (2√2- √3)/(2√2-2√3) = a+b√24 (ii) (4+ √2)/(2+ √2)=a-√b
(iii) (4+3√5)/(4-3√5)=a+b√5
4) If √2= 1.414, the find the value of:
(i) √8+ √50+ √72+ √98
(ii) 3√32-2√50+4√128-20√18
5) If √3= 1.732, then find the value of:
(i) √27+ √75+ √108-√243
(ii) 5√12-3√48+6√75+7√108
6) Simplify:
(i) ∛24+∛81- ∛192 (ii) 7√6-√252-√294+6√7
7) Find the value of 6/(√5-√3). Use(√3=1.732 and √5=2.236).
8) Simplify :
(i) 1/(2+√3)+ 2/(√5-√3)+1/(2-√5) (ii) 2/(√5+√3)+1/(√3+√2)-3/(√5+√2)
(iii) (3√2-2√3)/(3√2+2√3)+ √12/(√3-√2) (iv) (7+3√5)/(3+√5)- (7-3√5)/(3-√5)
(v) (7√3)/(√10+√3)- (2√5)/(√6-√5)-(3√2)/(√15-3√2)
9) If a = (3+√5)/2, then find the value of a^2+1/a^2 ?
10) If a = 5+2√6 and b = 1/a, then find the value of a2+b2?
11) If x = 1-√2 then find the value of
(i) x+1/x with a rational denominator
(ii) x^2+1/x^2 with a rational denominator
12) Find the value of a and b in the following :
(i) (2√6-√5)/(√45-√24)=a+b√30 (ii) (5+√3)/(7-4√3)=a+√3 b
(iii) (1+√6)/(3-√6)=a+b√6 (iv) (√5-2)/(√5+2)-(√5+2)/(√5-2)=a-b√5
(v) (3+√8)/(3-√8)+ (3-√8)/(3+√8)=a+b√2
13) If x = 2+√3, find the value of x^3+1/x^3 ?
14) If x = 3+√8, then find the value of x^2+1/x^2 ?
15) If x=(√3+1)/2, then find the value of 4x3 + 2x2 - 8x + 7 ?
16) Simplify : √6/(√2+√3)+(3√2)/(√6+√3)-(4√3)/(√6+√2)?
17) Simplify : 1/(√4+√5)+1/(√5+√6)+1/(√6+√7)+1/(√7+√8)+1/(√8+√9)?
18) If p=(2-√5)/(2+√5) and q=(2+√5)/(2-√5), then find the values of :
(i) p+q (ii) p-q (iii) p2+q2 (iv) p2-q2
19) If x=(√2-1)/√(2+1) and y=(√2+1)/(√2-1), then find the value of x2+5xy+y2?
