Question

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Answer 1

Question 1-

Find the cube root of (-0.064 × 0.729)

Answer -

$\begin{gathered}\begin{gathered} \longmapsto \rm { \sqrt[3]{ - 0.064} = - 0.4 }\\ \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered} \longmapsto \rm { \sqrt[3]{ 0.729} = 0.9}\\ \end{gathered} \end{gathered}$

now

$\begin{gathered}\begin{gathered} \longmapsto \rm { - 0.4 \times 0.9 }\\ \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered} \longmapsto \rm { - 0.36 }\\ \end{gathered} \end{gathered}$

Question 2-

estimate the cube root of 3,000

Answer -

Formula -

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

Where

• x = 3000
• y = 14 [ 14³ = 2744 and 2744 is the nearest perfect cube that is less than 3000]

$\begin{gathered} \begin{gathered}\\ \tt \mapsto \sqrt[3]{3000} = 14 \times \left(\frac{( {14}^{3} + 2 \times 3000)}{( {2 \times 14}^{3} + 3000)} \right)\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ \tt \mapsto \sqrt[3]{3000} = 14.4224 \: approx\end{gathered}\end{gathered}$

Question 3-

Find the least number by which 750 should be multiplied so that it becomes a perfect cube. also find the least number by which 750 should be divided so that it becomes a perfect cube .

Answer-

750

Prime factorising 750, we get,

750 = 3 × 2 × 5 × 5 × 5

750 = 3¹ × 2¹ × 5³

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of 3 is 1 and power of 5 is 3 and the power of other 2 is 1 .

so , The smallest number (3*3*2*2 = 36 ) should be multiply by 750 to make it perfect cube .

and , The smallest number (3*2 = 6) should be divided by 6655 to make it perfect cube .

Question 4-

The volume of a cube is 17.576 cm³ . find the length of each edge.

Answer-

Let -

volume of cube root be a³

then -

$\dashrightarrow\sf \: {a}^{3} = {17.576 }^{3}$

and

$\dashrightarrow\sf \: {a} = 2.6$

as 2.6 × 2.6 × 2.6 = 17.576

Therefore,

length of its edge = 2.6 cm

Question 5-

show that ³√125 × ³√216 = ³√125×216

Answer -

LHS -

$\begin{gathered} \begin{gathered}\\ \tt \mapsto \sqrt[3]{125} \times \sqrt[3]{216} \end{gathered} \end{gathered}$

$\begin{gathered} \begin{gathered}\\ \tt \mapsto \sqrt[3]{ 5 \times 5 \times 5 } \times \sqrt[3]{ 6 \times 6 \times 6 } \end{gathered} \end{gathered}$

$\begin{gathered} \begin{gathered}\\ \tt \mapsto {5 } \times {6} \end{gathered} \end{gathered}$

$\begin{gathered} \begin{gathered}\\ \tt \mapsto 30 \end{gathered} \end{gathered}$

RHS -

$\begin{gathered} \begin{gathered}\\ \tt \mapsto \sqrt[3]{{125} \times {216}} \end{gathered} \end{gathered}$

$\begin{gathered} \begin{gathered}\\ \tt \mapsto \sqrt[3]{5 \times 5 \times 5 \times 6 \times 6 \times 6} \end{gathered} \end{gathered}$

$\begin{gathered} \begin{gathered}\\ \tt \mapsto {5 \times 6} \end{gathered} \end{gathered}$

$\begin{gathered} \begin{gathered}\\ \tt \mapsto 30 \end{gathered} \end{gathered}$

LHS = RHS

Hence , shown

Answer 2

Question 1-

Find the cube root of (-0.064 × 0.729)

Answer -

$\begin{gathered}\begin{gathered} \longmapsto \rm { - 0.36 }\\ \end{gathered} \end{gathered}$

Question 2-

estimate the cube root of 3,000

Answer -

$\begin{gathered}\begin{gathered}\\ \tt \mapsto \sqrt[3]{3000} = 14.4224 \: approx\end{gathered}\end{gathered}$

Question 3-

Find the least number by which 750 should be multiplied so that it becomes a perfect cube. also find the least number by which 750 should be divided so that it becomes a perfect cube .

Answer-

36 and 6

Question 4-

The volume of a cube is 17.576 cm³ . find the length of each edge.

Answer-

2.6 cm