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Simplifying cube roots Quiz 2

mathematics

 Find the correct cube root of the number 0.018609625.

 Convert decimal into division form. Use tricks to find the unit’s place of cube root. Since, 5 is the last number in 18609625, so its cube root will also have 5 in the unit's place. Then find the nearest cube root to the number 18609 which will become the rest of the ten’s and hundredth place of the required number.

  $\begin{align} & \text{Convert }0.018609625=\dfrac{18609625}{1000000000}.\\ & \text{Now, consider }18609625. \\ & \text{Unit’s place of }18609625 = 5 \\ & \text{So, unit’s place of cube root = 5 and nearest cube number to }18609 = 17576 \,\,\,\,\,\,\,\,\,(\text{being a cube of }26)\\ & \Rightarrow \text{Cube root: }\sqrt[3]{0.018609625}=\sqrt[3]{\dfrac{18609625}{1000000000}}=0.265\end{align}$ 

 Try to figure out the cube root of $\sqrt[3]{15569+\sqrt[3]{175590+\sqrt[3]{17576}}}$. 

 Solve the cube. Since, 6 is the last number in 17576 so, its cube root will also have 6 in the unit's place. Then find the nearest cube root to the number 17 which will become the rest of the ten’s and hundredth place of the required number. Then add. Similarly, find cube root of 175616, 15625.

  $\begin{align} & \text{First find the cube root of }17576. \\ & \text{Unit’s place of 17576 gives unit’s place of its cube root }= 6. \\ & \text{Nearest cube number which divides 17 is 8}\,\,\,\,\,\,\,\, (\text{being a cube of 2}).\\ & \text{So, cube root of }17576 = 26.\\ & \Rightarrow \sqrt[3]{15569+\sqrt[3]{175590+\sqrt[3]{17576}}}=\sqrt[3]{15569+\sqrt[3]{175590+26}}\\ & \text{Follow the above steps and find the cube root of }17576 + 26 = 175616\text{ which is }56.\\ & \Rightarrow \sqrt[3]{15569+\sqrt[3]{175590+\sqrt[3]{17576}}}=\sqrt[3]{15569+56} \\ &  \Rightarrow \sqrt[3]{15569+\sqrt[3]{175590+\sqrt[3]{17576}}}=\sqrt[3]{15625}\\ & \text{Similarly, the cube root of 15625 is 56.}\end{align}$

 Find the value of $y$ such that $36{{\left( 281011375 \right)}^{\frac{1}{3}}}=0.25y$.

 Solve cube root first by considering the unit’s digit as 5 as that of the unit’s digit as 281011375. Then, find the nearest cube number to divide 281011. This cube number will be the tens and hundredths digit of the cube root of 281011375.

 $\begin{align} & \text{Consider }281011375.\\ & \text{Since, its unit’s place is 5 so, the unit’s place of it’s cube root will be 5. Also, the nearest cube number to divide }281011 = 274625 \,\,\,\,\,\,\,\,(\text{being a cube of 65}).\\ & \text{So, the cube root of }281011375 = 655. \\ & \Rightarrow 36{{\left( 281011375 \right)}^{\frac{1}{3}}}=0.25y \\ &  \Rightarrow y=94320\end{align}$ 

 Try to simplify $\dfrac{{{\left( 17173512 \right)}^{\frac{1}{3}}}\times {{\left( 140608 \right)}^{\frac{1}{3}}}}{{{\left( 592704 \right)}^{\frac{1}{3}}}+{{\left( 15438249 \right)}^{\frac{1}{3}}}}$.

 Find cube roots and then solve. The cube roots can be found by noticing the last digit of the given number and selecting the nearest cube number which can divide the given number, ${$take the number by ignoring the last three digits e.g., if it is 45123 so find the nearest cube root to the number 45$)$. 

 $\begin{align} & \text{Consider the number 17173512 and check its unit digit. Since, it is one so its cube’s unit’s digit will be 8. The nearest cube number which divides 17173 is 15625} \,\,\,\,\,\,\,\,\,(\text{being the cube root of 25}).\\ & \text{So, the cube root of }17173512 = 258. \\ & \text{Similarly, get the cube root of the rest of numbers. }\\ & \Rightarrow \dfrac{{{\left( 17173512 \right)}^{\frac{1}{3}}}\times {{\left( 140608 \right)}^{\frac{1}{3}}}}{{{\left( 592704 \right)}^{\frac{1}{3}}}+{{\left( 15438249 \right)}^{\frac{1}{3}}}}=\dfrac{258\times 52}{84+249}=40.288\end{align}$ 

 Which of the following cube roots satisfies the number 16387064?

 Solve the cube root first by considering the unit’s digit as 4 as that of the unit’s digit as 16387064. Then, find the nearest cube number to divide 16387. This cube number will be the tens and hundredth digit of the cube root of 16387064.

 $\begin{align} & \text{Unit’s place of 16387064 = 4, so its cube root will also have unit’s place = 4. Find the smallest cube number nearer to 16387 = 15625.}\,\,\,\,\,\,\,\,(\text{Being the cube of 25 it will become the tenth and hundredth places of the cube root of 16387064})\\ & \Rightarrow \sqrt[3]{16387064}=254\end{align}$