Simplify √(50) + √(18).

Simplification & Approximation · Question 45 of 71

Question 45

EasyOriginal question

Simplify $\sqrt{50} + \sqrt{18}$ .

2\sqrt{17}

Correct answerYour answer

15\sqrt{2}

Correct answerYour answer

4\sqrt{17}

Correct answerYour answer

8\sqrt{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$ and $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$ .
Like surds add like terms: $5\sqrt{2} + 3\sqrt{2} = 8\sqrt{2}$ .

Worth noting

$\sqrt{a} + \sqrt{b}$ is not $\sqrt{a + b}$ : $\sqrt{68} = 2\sqrt{17}$ is the tempting wrong answer. Multiplying the coefficients 5 and 3 gives $15\sqrt{2}$ .

Concept: Adding surds after simplifying to a common surd
Typical timeTypical: 40 s
Your timeYours: —

The rule this testsPowers, roots and surds

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Simplify 50+18\sqrt{50} + \sqrt{18}50​+18​.

Explanation

Simplify $\sqrt{50} + \sqrt{18}$ .