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Simplify the expression: (sqrt(2) + sqrt(5)) / sqrt(3)

Mathematics

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Answer

6+153\frac{\sqrt{6} + \sqrt{15}}{3}

Step-by-step solution

5 steps

  1. Write the given expression.

    2+53\frac{\sqrt{2} + \sqrt{5}}{\sqrt{3}}

  2. Rationalize the denominator by multiplying the numerator and denominator by 3\sqrt{3}.

    2+53×33\frac{\sqrt{2} + \sqrt{5}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}

  3. Multiply the terms in the numerator and the denominator.

    (2+5)×33×3\frac{(\sqrt{2} + \sqrt{5}) \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}

  4. Distribute 3\sqrt{3} in the numerator and simplify the denominator.

    2×3+5×33\frac{\sqrt{2} \times \sqrt{3} + \sqrt{5} \times \sqrt{3}}{3}

  5. Simplify the square roots in the numerator.

    2×3+5×33\frac{\sqrt{2 \times 3} + \sqrt{5 \times 3}}{3} 6+153\frac{\sqrt{6} + \sqrt{15}}{3}
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