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Find the cube roots of the following perfect cubes using estimation
a. 592704
b. 24389
c. 438976
d. 91125
full solution
Answers
Answer:
84 is the cube root of 592704
Answer:
Given : An A.P 3rd Term = {\sf{a_{3}}}a
3
= 4 & 9th Term = {\sf{a_{9}}}a
9
= -8.
To Find : Find the term of the corresponding A.P is 0 ?
_________________________
Solution : Let the nth term to be x.
~
\underline{\frak{As ~we~ know ~that~:}}
As we know that :
\boxed{\sf\purple{a_{n}~=~a~+~\bigg(n~-~1\bigg)d}}
a
n
= a + (n − 1)d
★
~
Where,
a = First Term
d = Common Difference
~
◗Here, a and b be the first term and common difference of the corresponding A.P respectively.
~
Therefore,
{\sf{a_{3}~=~4}}a
3
= 4
{\sf{a~+~2d~=~4~~~~~~~~~~~~~~~~~~~~~~~\bigg\lgroup{1~Eqⁿ}\bigg\rgroup}}a + 2d = 4
⎩
⎪
⎪
⎪
⎧
1 Eqⁿ
⎭
⎪
⎪
⎪
⎫
{\sf{a_{9}~=~- 8}}a
9
= −8
{\sf{a~+~8d~=~- 8~~~~~~~~~~~~~~~~~~~~\bigg\lgroup{2~Eqⁿ}\bigg\rgroup}}a + 8d = −8
⎩
⎪
⎪
⎪
⎧
2 Eqⁿ
⎭
⎪
⎪
⎪
⎫
~
Substituting (1) From (2)
\dashrightarrow{\sf{6d~=~- 12}}⇢6d = −12
\dashrightarrow\boxed{\sf{d~=~- 2}}⇢
d = −2
~
Putting Value of d in (1)
\dashrightarrow{\sf{a~+~2~×~(- 2)~=~4}}⇢a + 2 × (−2) = 4
\dashrightarrow\boxed{\sf{a~=~8}}⇢
a = 8
~
Now,
Let nth term of A.P. is zero :
~
Henceforth,
\qquad{\sf:\implies{a_{n}~=~0}}:⟹a
n
= 0
\qquad{\sf:\implies{a~+~(n~-~1)d~=~0}}:⟹a + (n − 1)d = 0
\qquad{\sf:\implies{8~+~(n~-~1)(- 2)~=~0}}:⟹8 + (n − 1)(−2) = 0
\qquad{\sf:\implies{8~-~2n~+~2~=~0}}:⟹8 − 2n + 2 = 0
\qquad{\sf:\implies{2n~=~10}}:⟹2n = 10
\qquad{\sf:\implies{n~=~\cancel\dfrac{10}{2}}}:⟹n =
2
10
\qquad:\implies{\underline{\boxed{\frak{\pink{n~=~5}}}}}:⟹
n = 5
★
~
Hence,
\therefore\underline{\bf{\underline{5th~term}}~\sf{of~the~A.P.~is~0}}∴
5th term
of the A.P. is 0