what is the formula of 1=1cube
3+5=2cube
7+9+11=3cube
13+15+17+19=4cube
Answers
Step-by-step explanation:
2n^4 - n² or n² (2n² - 1) Solution: The nth term of the given series 1³ + 5³ + 7³ +… ... + (1+3+5+7) +… (1+3+5+7+9+11+13+15+17+19) =? 4,085 ...
Answer:It is known that,
nth root of a is expressed as a1/n.
(1) Fifth root of 13
= (13)1/5
(2) Sixth root of 9
= (9)1/6
(3) Square root of 256
= (256)1/2
(4) Cube root of 17
= (17)1/3
(5) Eighth root of 100
= (100)1/8
(6) Seventh root of 30
= (30)1/7
Page No 15:
Question 2:
Write in the form 'nth root of a' in each of the following numbers.
(1) (81)14
(2) 4912
(3) (15)15
(4) (512)19
(5) 100119
(6) (6)17
ANSWER:
It is known that,
nth root of a is expressed as a1/n.
(1) (81)14
= Fourth root of 81
(2) (49)12
= Square root of 49
(3) (15)15
= Fifth root of 15
(4) (512)19
= Ninth root of 512
(5) (100)119
= Nineteenth root of 100
(6) (6)17
= Seventh root of 6
Page No 16:
Question 1:
Complete the following table.
Sr. No. Number Power of the root Root of the power
(1) (225)32 Cube of square root of 225 Square root of cube of 225
(2) (45)45
(3) (81)67
(4) (100)410
(5) (21)37
ANSWER:
Sr. No. Number Power of the root Root of the power
(1) (225)32 cube of square root of 225 square root of cube of 225
(2) (45)45 4th power of 5th root of 45 5th root of 4th power of 45
(3) (81)67 6th power of 7th root of 81 7th root of 6th power of 81
(4) (100)410 4th power of 10th root of 100 10th root of 4th power of 100
(5) (21)37 cube of 7th root of 21 7th root of cube of 21
Page No 16:
Question 2:
Write the following numbers in the form of rational indices.
(1) Square root of 5th power of 121
(2) Cube of 4th root of 324
(3) 5th root of square of 264
(4) Cube of cube root of 3
ANSWER:
It is known that,
am/n = (am)1/n means 'nth root of mth power of a'.
am/n = (a1/n)m means 'mth power of nth root of a'.
(1) Square root of 5th power of 121
={(121)5}12=(121)52
(2) Cube of 4th root of 324
={(324)14}3=(324)34
(3) 5th root of square of 264
={(264)2}15=(264)25
(4) Cube of cube root of 3
={313}3=333
Page No 18:
Question 1:
Find the cube roots of the following numbers.
(1) 8000
(2) 729
(3) 343
(4) −512
(5) −2744
(6) 32768
ANSWER:
(1) To find the cube root of 8000, let us factorise 8000 first.
8000=2×2×2×2×2×2×5×5×58000=4×4×4×5×5×5 = 43×53=(4×5)3 [am×bm=(a×b)m]8000=(20)3∴8000−−−−√3=20
(2) To find the cube root of 729, let us factorise 729 first.
729=3×3×3×3×3×3729=(3×3)×(3×3)×(3×3)=(3×3)3=93∴729−−−√3=9
(3) To find the cube root of 343, let us factorise 343 first.
343=7×7×7=73∴343−−−√3=7
(4) To find the cube root of −512, let us factorise 512 first.
512=2×2×2×2×2×2×2×2×2512=(2×2×2)×(2×2×2)×(2×2×2)=8×8×8×=83−512=(−8)×(−8)×(−8)=(−8)3∴−512−−−−√3=−8
(5) To find the cube root of −2744, let us factorise 2744 first.
2744=2×2×2×7×7×72744=(2×7)×(2×7)×(2×7)=(2×7)3=143−2744=(−14)3∴−2744−−−−−√3=−14
(6) To find the cube root of 32768, let us factorise 32768 first.
32768=2×2×2×2×2×2×2×2×2×2×2×2×2×2×232768=(2×2×2×2×2)×(2×2×2×2×2)×(2×2×2×2×2)=32×32×32=(32)3∴32768−−−−−√3=32
Page No 18:
Question 2:
Simplify:
(1) 27125−−−√3
(2) 1654−−√3
ANSWER:
(1) 27125−−−√3=3×3×35×5×5−−−−−√3=3353−−√3=(35)3−−−−√3 [ambm=(ab)m]=35
(2) 1654−−√3=2×2×2×22×3×3×3−−−−−−−√3=2×2×23×3×3−−−−−√3=2333−−√3=(23)3−−−−√3 [ambm=(ab)m]=23
Page No 18:
Question 3:
If 729−−−√3 = 9 then 0.000729−−−−−−−√3 = ?
ANSWER:
It is given that,
729−−−√3=90.000729−−−−−−−√3=7291000000−−−−−√3=729√31000000√3=93√3(100)3√3=9100=0.09