Estimating the Cube Root Range for 150
To find the range where the cube root of 150 lies, we need to find two consecutive integers whose cubes bracket 150.
Cube Root Estimation
Let the number be '$N = 150$'. We are looking for a value '$x$' such that $x^3 = N$. We can test the cubes of integers:
- Calculate the cube of 5: $5^3 = 5 \times 5 \times 5 = 125$.
- Calculate the cube of 6: $6^3 = 6 \times 6 \times 6 = 216$.
Determining the Range
We observe that 150 falls between the calculated cubes:
$125 < 150 < 216$Substituting the integer cubes back:
$5^3 < 150 < 6^3$Taking the cube root of all parts of the inequality:
$\sqrt[3]{5^3} < \sqrt[3]{150} < \sqrt[3]{6^3}$ $\implies 5 < \sqrt[3]{150} < 6$Therefore, the cube root of 150 lies between 5 and 6.
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Important Questions from Cube and Cube Root
If 5 \(\sqrt{3}\) + \(\sqrt{75}\) = 17.32, then the value of 14 \(\sqrt{3}\) + \(\sqrt{108}\) is:
Find the value of (25)3 + (-29)3 + (4)3
The value of \(\frac{\sqrt[3]{-2744} \times \sqrt[3]{-216}}{\sqrt[3]{\frac{64}{729}}}\) is:
A number is cube of 53. When 7 times of 57 is subtracted from the number, then the resultant number which is formed will be divisible by:
The sum of a positive number and its cube is 1740. What is the value of the number?
