Square Roots - Pre-Algebra Step by Step

Evaluate perfect square roots and simplify non-perfect roots by factoring out perfect squares.

square-roots To simplify √n: - If n is a perfect square, state √n = k. - Otherwise factor n = a · b where a is the largest perfect square factor, then √n = √a · √b = k√b.

Example

Use perfect-square factors to evaluate and simplify square roots.

highlighted = computed this step

Step 1 — Perfect square

Set up the expression.

\sqrt{64}

Step 2 — Check the square

Check the square: 8^2 = 64.

\hlmath{8^{2}} = 64

Step 3 — Take the square root

Take the square root: sqrt(64) = 8.

\sqrt{64} = \hl{8}

Step 4 — Simplify a radical

Set up the expression.

\sqrt{50}

Step 5 — Factor the radicand

Factor the radicand: 50 = 25 x 2.

50 = \hl{25} \times \hl{2}

Step 6 — Root the square factor

Take out the square factor: sqrt(25) = 5.

\sqrt{25} = \hl{5}

Step 7 — Result

Keep the leftover under the root: 5sqrt(2).

\sqrt{50} = \hlmath{5\sqrt{2}}