Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots3 Marks
Question
Find the cube root of the following numbers:
-27 × 2744
✓
Answer
Property:
For any two integers a and b, $\sqrt[3]{\text{ab}}=\sqrt[3]{\text{a}}\times\sqrt[3]{\text{b}},$
From the above property, we have:
$\sqrt[3]{-27\times2744}$
$=\sqrt[3]{-27}\times\sqrt[3]{2744}$
$-=\sqrt[3]{1728}\times\sqrt[3]{216}$ (For any positive integer $\text{x},\sqrt[3]{-\text{x}}=-\sqrt[3]{\text{x}}$)
Cube root using units digit:
Let us consider the number 2744.
The unit digit is 4; therefore, the unit digit in the cube root of 2744 will be 4.
After striking out the units, tens, and hundreds digits of the given number, we are left with 2.
Now, 1 is the largest number whose cube is less than or equal to 2.
Therefore, the tens digit of the cube root of 2744 is 1
$\therefore\sqrt[3]{2744}=14$
Thus
$\sqrt[3]{-27\times2744}$
$=-\sqrt[3]{27}\times\sqrt[3]{2744}$
$=-3\times6=-42$
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