Multiplying base by fraction for fractional indices H
"The Fraction Fumble"
The Mistake in Action
Evaluate $16^{\frac{1}{2}}$
Wrong: $16 \times \frac{1}{2} = 8$
Why It Happens
Students don't recognise fractional indices as roots. They multiply the base by the fraction instead.
The Fix
A fractional index means a root:
$$a^{\frac{1}{n}} = \sqrt[n]{a}$$
So $a^{\frac{1}{2}} = \sqrt{a}$ (square root)
$$16^{\frac{1}{2}} = \sqrt{16} = 4$$
Memory aid: "Power of a half = square root" "Power of a third = cube root"
Spot the Mistake
Can you identify where this student went wrong?
Evaluate $16^{\frac{1}{2}}$
$= 16 \times \frac{1}{2} = 8$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: