Here we are trying to give the Class 9 Maths Problems for Number System. This contains tough/difficult questions on number system class 9. I hope you like the questions
Question 1
Find the value of each of the Following
a. 21/4×21/5
b. 16−3/4
c. 3√2.4√212√32
d. 15√6+√216
e. 115/2113/2
f. 53/273/2
g. √162√2
h. (8+√3)(8−√3)
Solution
a. 21/4×21/5=214+15=29/20
b. 16−3/4=(24)−3/4=18
c. 3√2.4√2.12√32=21/3.21/4.25/12=213+14+512=2
d. 15√6+√216=15√6+√62×6=15√6+6√6=21√6
e. 115/2113/2=1152−32=11
f. 53/273/2=(5×7)3/2=(35)3/2
g. √162√2=9√2√2=9
h. (8+√3)(8−√3)=(8+√3)(8−√3)×(8+√3)(8+√3) =161[64+3+16√3]=161(67+16√3)
Question 2
Simplify the below expression
a. 4√81−83√216+155√32+√225
b. 64−1/3[641/3−642/3]
c. 4216−2/3+1256−3/4+2243−1/5
Question 3
Find the value of p and q such that 5+√37+2√3=p+q√3 Solution 5+√37+2√3 =5+√37+2√3×7−2√37−2√3 =137×[35−10√3+7√3−6] =137×[29−3√3] =2937−337√3
Now 2937−337√3=p+q√3
so p=2937 and q=−337
Question 4
If x=1+√3
and y=1x
Find the value of
i. x2+y2
ii. x2−y2
iii. (x+y)2
iv. x−y
Solution x=1+√3 x2=(1+√3)2=2(2+√3) y=1x=11+√3=12(√3−1) y2=12(2−√3)
Now,
i. x2+y2=2(2+√3)+12(2−√3) =12(10+3√3)
ii. x2−y2=2(2+√3)−12(2−√3) =12(8+5√3)
iii. (x+y)2=(1+3√32)2=14[28+6√3]=12(14+3√3)
iv. x−y=3+√32
Question 5
Write the following in decimal form and say what kind of decimal expansion each has:
(i) 19100
(ii) 13
(iii) 1112
(iv) 113
(v) 313
(vi) 111400
Solution
Question 6
Find the value of 11+√2+1√2+√3+1√3+√4+...+1√8+√9 Solution 11+√2+1√2+√3+1√3+√4+...+1√8+√9 =1√2+1+1√3+√2+1√4+√3+...+1√9+√8 =1√2+1×√2−1√2−1+1√3+√2×√3−√2√3−√2+1√4+√3×√4−√3√4−√3+...+1√9+√8×√9−√8√9−√8 =(√2−1)+(√3−√2)+(√4−√3).....+(√9−√8)=2
Question 7
Find the value of √3+2√2+√3−2√2√√3+1−2√√3−1 Solution =√(√2+1)2+√(√2−1)2√√3+1−2√√3−1 =√2+1+√2−1√√3+1−2√√3−1 =2√2√√3+1−2√√3−1 =2√2−2√2√√3+1
=0
Question 8
Find the value of 12+√3+2√5−√3+12−√5 Solution =2−√3+√5+√3−2+√5=0
Summary
This Class 9 Maths Problems for Number System with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.