Question

Find the cube roots of the following numbers:-
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8000
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729
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343
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Answer 1

Answer:

the answer is

Step-by-step explanation:

1) 8000 cube root = 20

2) 729 cube root = 9

3) 343 cube root = 7

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Answer 2

$\Large{\underbrace{\sf{\green{Required \; Solution:}}}}$

To find the cubes of 8000 , 729  & 343.

⬩ 8000

    $\Large{ \begin{array}{c|c} \tt 2 & \sf{ 8000} \\ \tt 2 & \sf { 4000} \\ \tt 2 & \sf{ 2000} \\ \tt 2 & \sf{ 1000} \\ \tt 2 & \sf{ 500} \\ \tt 2 & \sf{ 250} \\ \tt 5 & \sf{ 125} \\ \tt 5 & \sf{ 25} \\ \tt 5 & \sf{ 5} \\ \tt & \sf{ 1} \\ \end{array}}$

Now,

8000 =

$\implies \sf{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5}$

$\implies \sf{ (2 \times 5) \times (2 \times 5) \times (2 \times 5) \times 2^3}$

$\implies \sf{(2 \times 5)^3 \times 2^3}$

$\implies \sf{(10)^3 \times 2^3}$

$\implies \sf{10^3 \times 2^3}$

$\implies \sf{ (10 \times 2)^3 } \dots \Big \langle \purple{\frak{a^m \times b^m = (a \times b)^m}} \Big \rangle$

$\implies \underline{\underline{\sf{ \; (20) \; }}}$

$\therefore \underline{\boxed{\sf{\orange{ \sqrt[\sf{3}]{\sf{8000}} = 20 }} }}$

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⬩ 729

    $\Large{ \begin{array}{c|c} \tt 3 & \sf{ 729} \\ \tt 3 & \sf { 243} \\ \tt 3 & \sf{ 81} \\ \tt 3 & \sf{ 27} \\ \tt 3 & \sf{ 9} \\ \tt 3 & \sf{ 3 } \\ \tt & \sf{ 1} \\ \end{array}}$

Now,

729 =

$\implies \sf{ 3 \times 3 \times 3 \times 3 \times 3 \times 3 }$

$\implies \sf{ ( 3 \times 3) \times ( 3 \times 3) \times ( 3 \times 3) }$

$\implies \sf{( 3 \times 3) ^3 }$

$\implies \underline{\underline{\sf{ \; (9)^3 \; }}}$

$\therefore \underline{\boxed{\sf{\orange{ \sqrt[\sf{3}]{\sf{729}} = 9 }} }}$

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⬩ 343

    $\Large{ \begin{array}{c|c} \tt 7 & \sf{ 343} \\ \tt 7 & \sf { 49} \\ \tt 7 & \sf{ 7} \\ \tt & \sf{ 1} \end{array}}$

Now,

343 =

$\implies \sf{ 7 \times 7 \times 7}$

$\implies \underline{\underline{\sf{ \; (7)^3 \; }}}$

$\therefore \underline{\boxed{\sf{\orange{ \sqrt[\sf{3}]{\sf{343}} = 7 }} }}$

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* ⁺◦﹆◞˚ ꒰ More to know ꒱

   

⋆ Law of Indices:

• $\sf{a^m \times a^n = a^{m + n}}$

• $\sf{a^m \div a^n = a^{m-n}}$

• $\sf{(a \times b)^m = a^m \times b^m}$

• $\sf{a^0 = 1}$

• $\sf{a^{-m} = \dfrac{1}{a^m}}$

• $\sf{(a^m)^n = a}$

• $\sf{\bigg( \dfrac{a}{b} \bigg)^m = \dfrac{a^m}{b^m}}$

• $\sf{ \bigg( \dfrac{a}{b} \bigg)^{-m} = \bigg( \dfrac{b}{a} \bigg)^m }$

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Apologies for mistakes <3