# Chapter 10 - Section 10.1 - Radical Expressions and Radical Functions - Exercise Set: 109

The perimeter of the triangle is closest to 18.

#### Work Step by Step

Take the sum of all the sides. $\sqrt {30}+\sqrt {10}+\sqrt {90}$ Approximate the values of the square roots based on the closest perfect square. ex. $\sqrt {30}\approx5.4$ because the nearest perfect squares are $\sqrt {25}$ and $\sqrt {36}$ (between 5 and 6) Repeat this approximation with the other square roots. $5.4+3.1+9.5\approx18$ Common mistake (this is illegal math): $\sqrt {30}+\sqrt {90}+\sqrt {10}=\sqrt{130}$ $\sqrt {130}\approx12$ (wrong) because $\sqrt {30}+\sqrt {90}+\sqrt {10}\ne\sqrt {30+90+10}$

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