If cube root of -2744 ÷ cube root of 0.008 =x then the value of x is
The Correct Answer and Explanation is:
o solve the expression −274430.0083=x\frac{\sqrt[3]{-2744}}{\sqrt[3]{0.008}} = x30.0083−2744=x, we begin by simplifying both the numerator and the denominator.
- Cube root of -2744:
The cube root of a negative number is negative. We need to find the cube root of 2744 and then apply the negative sign. First, find the cube root of 2744: 27443=14\sqrt[3]{2744} = 1432744=14 This is because: 14×14×14=274414 \times 14 \times 14 = 274414×14×14=2744 Hence, the cube root of -2744 is: −27443=−14\sqrt[3]{-2744} = -143−2744=−14 - Cube root of 0.008:
To find the cube root of 0.008, we need to express 0.008 as a fraction: 0.008=81000=231030.008 = \frac{8}{1000} = \frac{2^3}{10^3}0.008=10008=10323 The cube root of this fraction is: 231033=2331033=210=0.2\sqrt[3]{\frac{2^3}{10^3}} = \frac{\sqrt[3]{2^3}}{\sqrt[3]{10^3}} = \frac{2}{10} = 0.2310323=3103323=102=0.2 - Putting it together:
Now, substitute the values we have found into the original expression: −274430.0083=−140.2\frac{\sqrt[3]{-2744}}{\sqrt[3]{0.008}} = \frac{-14}{0.2}30.0083−2744=0.2−14 Dividing -14 by 0.2: −14÷0.2=−14×5=−70-14 \div 0.2 = -14 \times 5 = -70−14÷0.2=−14×5=−70 Thus, the value of xxx is: x=−70x = -70x=−70
Explanation:
To calculate cube roots, we need to determine a number that, when multiplied by itself three times, gives the original number. In the case of negative numbers, the cube root will also be negative. For example, the cube root of -2744 is -14 because (−14)×(−14)×(−14)=−2744(-14) \times (-14) \times (-14) = -2744(−14)×(−14)×(−14)=−2744. Similarly, when finding the cube root of 0.008, we express it as a fraction of cubes (23103\frac{2^3}{10^3}10323), and then the cube root of each part is calculated separately, resulting in 0.2. After that, we simply divide the two results to get the final value of xxx, which is -70.
