Question
The cube root of 150 will lie between:
This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper (8-Mar-2021) (Shift 2)
The correct answer is
5 and 6
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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