Math · College algebra · Worked example

Simplify and combine radicals

Simplify √72 + √50 − √8.

\sqrt{72} + \sqrt{50} - \sqrt{8}

Find the largest perfect-square factors

72 = 36 · 2, 50 = 25 · 2 and 8 = 4 · 2. Each radicand has a perfect-square factor times 2.

√72 = 6√2, √50 = 5√2 and √8 = 2√2.

6 \sqrt{2} + 5 \sqrt{2} - 2 \sqrt{2}

All three terms are multiples of √2, so add their coefficients: 6 + 5 − 2 = 9.

(6 + 5 - 2) \sqrt{2} = 9 \sqrt{2}

√72 + √50 − √8 ≈ 8.485 + 7.071 − 2.828 = 12.728, and 9√2 ≈ 12.728.

√72 + √50 − √8 = 9√2.

9 \sqrt{2}

Rationalize the denominator of 6/√3.

Show the answer and explanation

Multiply the top and bottom by √3: 6√3/3 = 2√3.

\frac{6}{\sqrt{3}} = \frac{6 \sqrt{3}}{3} = 2 \sqrt{3}

Open the rows in Math and change √8 to √18: the checker expects 6√2 + 5√2 − 3√2 = 8√2.

Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.

Make it concrete

Open the example inputs, change a value and keep a useful result on your board.

Your existing work stays on this device. Examples open as editable copies.