Question

please solve all above questions and also show the solution how you got the answer please solve it please​

Answer 1

Answer 6 -

Formula - $\begin{gathered}\\ \tt \mapsto \sqrt[3]{x} = y \times \left(\frac{( {y}^{3} + 2x)}{( {2y}^{3} + x)} \right)\end{gathered}$

i) 3500

Where

• x = 3500
• y = 15 [ 15³ = 3375 and 3375 is the nearest perfect cube that is less than 3500]

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{3500} = 15 \times \left(\frac{( {15}^{3} + 2 \times 3500)}{( {2 \times 15}^{3} + 3500)} \right)\end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{3500} = 15.1829 \: approx\end{gathered}$

ii) 5000

Where

• x = 5000
• y = 17 [ 17³ = 4913 and 4913 is the nearest perfect cube that is less than 5000]

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{5000} = 17 \times \left(\frac{( {17}^{3} + 2 \times 5000)}{( {2 \times 17}^{3} + 5000)} \right)\end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{5000} = 17.099 \: approx\end{gathered}$

Answer 7 -

1) 4.096 = 1.6

2) 9.261 = 2.13

3) 42.875 = 3.5

4) 91.125 = 4.5

5) 110.592 = 4.8

Answer 8 -

1) 2 93/125

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{2 \frac{93}{125} } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{\frac{343}{125} } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{\frac{7 \times 7 \times 7}{5 \times 5 \times 5} } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {\frac{7 }{5 } } \end{gathered}$

2) -0.125

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{-0.125} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{-0.5 \times -0.5 \times -0.5} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {-0.5} \end{gathered}$

3) -1 271/729

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{-1 \frac{271}{729} } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{\frac{-458}{729} } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {\frac{-7.708}{9} } \end{gathered}$

4) -2 10/27

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{-2 \frac{10}{27} } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{\frac{-44}{27}} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {\frac{-3.53}{3} } \end{gathered}$

5) -0.001

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{ -0.001} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{-0.1 \times -0.1 \times -0.1} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {-0.1} \end{gathered}$

Answer 9-

1) ³√27 × ³√64 = ³√27×64

LHS -

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{27} \times \sqrt[3]{64} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{3 \times 3 \times 3 } \times \sqrt[3]{4 \times 4 \times 4} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {3 } \times {4 } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto 12 \end{gathered}$

RHS -

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{{27} \times {64}} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{3 \times 3 \times 3 \times 4 \times 4 \times 4} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {3 \times 4} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto 12 \end{gathered}$

LHS = RHS

Hence , shown

2) ³√216 × ³√8 = ³√216×8

LHS -

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{216} \times \sqrt[3]{8} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{6 \times 6 \times 6 } \times \sqrt[3]{ 2 \times 2 \times 2 } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {6 } \times {2} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto 12 \end{gathered}$

RHS -

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{{216} \times {8}} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{6 \times 6 \times 6 \times 2 \times 2 \times 2} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {6 \times 2} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto 12 \end{gathered}$

LHS = RHS

Hence , shown

3) ³√125 × ³√1000 = ³√125×1000

LHS -

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{125} \times \sqrt[3]{1000} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{ 5 \times 5 \times 5 } \times \sqrt[3]{ 10 \times 10 \times 10 } \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {5 } \times {10} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto 50 \end{gathered}$

RHS -

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{{125} \times {1000}} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto \sqrt[3]{5 \times 5 \times 5 \times 10 \times 10 \times 10} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto {5 \times 10} \end{gathered}$

$\begin{gathered}\\ \tt \mapsto 50 \end{gathered}$

LHS = RHS

Hence , shown

Note - Question 5 is in attachment

Answer 2

Answer:

here is your answer Tina!!

purple you dear keep smiling:)