Grade 11 Exponents and surds

Rational exponents, surd arithmetic, and equations with the unknown in an exponent or under a root.

Gr 11 Term 1 - Exponents and surdsTerm 1 - 3 weeks (CAPS)

Practise Exponents and surds in the app →

What gets asked

• Simplify an expression whose exponents are fractions.
• Evaluate a power like $8^{2/3}$ without a calculator.
• Add or multiply surds and give the answer in simplest surd form.
• Solve an equation with the unknown under a square root.

You must be able to

• Read $a^{m/n}$ as the $n$th root of $a$, raised to the power $m$.
• Simplify each surd to like form before adding coefficients.
• Raise both sides of $x^{m/n}=c$ to the reciprocal power $n/m$.
• After squaring both sides of a surd equation, substitute the candidates back.

Traps that cost marks

• Adding the numbers under the roots, as if root 2 plus root 8 were root 10. Simplify first: root 8 is 2 root 2, so the sum is 3 root 2 - only like surds add.
• Squaring a surd equation term by term instead of side by side. Square each whole side once, then solve the quadratic that appears.
• Taking the root with the numerator and the power with the denominator in $a^{m/n}$. The denominator names the root; the numerator is the ordinary power.

Worked example