Which is bigger: the cube root of 54 or the square root of 18?
Explanation
In this type of problem it will be easier to approximate than to solve for the actual roots of both numbers. Factor down the numbers by making use of as many repeated small numbers.
Cube root [54] = cube root \([2 \times 3 \times 3 \times 3]\)= cube root \([(3 \times 3 \times 3)(2)]\)
Cube root [54] = 3 cube root [2]
Square root [18] = square root \([2 \times 3 \times 3]\)= square root \([(3 \times 3)(2)]\)
Square root [18] = 3 square root [2]
Compare the two values:
3 cube root [2] ? 3 square root [2]
Cube root [2] < square root [2]
Square root [2] is bigger than cube root [2]; therefore, square root of 18 is the larger number.
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