Common Core · High school
HSN-RN.A.2
High school — Rewrite expressions involving radicals and rational exponents using the properties of exponents.
The 3 skills that cover it
- Simplifying RadicalsWrite a square root in simplest form by pulling out perfect-square factors, then add, multiply and divide radicals, and clear a root from a denominator.Read the lesson →
- Special Right TrianglesUse the 45-45-90 and 30-60-90 side ratios to find exact side lengths written with radicals, and recognise the two triangles inside squares, equilateral triangles and hexagons.Read the lesson →
- Rational Exponents & Radical EquationsRead a fractional exponent as a root, move between radical and exponent form, simplify with the exponent rules, and solve equations with a variable under a root, checking for solutions the squaring step invents.Read the lesson →
What a student should be able to do
- Simplify a square root such as sqrt(50) to 5 sqrt(2) by factoring out the largest perfect square.
- Multiply and divide square roots, and simplify the product.
- Add and subtract like radicals after simplifying each one.
- Rationalise a denominator such as 6 / sqrt(3).
- Find the hypotenuse or a leg of a 45-45-90 triangle exactly.
- Find any side of a 30-60-90 triangle from any other side exactly.
- Recognise special right triangles inside squares, equilateral triangles and regular hexagons.
- Solve problems whose answers are exact lengths in simplest radical form.
- Evaluate an expression with a rational exponent such as 82/3, and take an nth root.
- Convert between radical form and rational-exponent form, and simplify using the exponent rules.
- Solve a radical equation by isolating the root and raising both sides to a power.
- Check every candidate in the original equation and reject extraneous solutions; state the domain of a radical function.