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Simplify the expression sqrt(108) + sqrt(125) - sqrt(75).

May 15, 2026Mathematics

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Answer

\sqrt{3} + 5\sqrt{5}

3 steps

Simplify each radical by finding the largest perfect square factor.
For $\sqrt{108}$ :
$\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}$
For $\sqrt{125}$ :
$\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}$
For $\sqrt{75}$ :
$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$
Substitute the simplified radicals back into the original expression.
$6\sqrt{3} + 5\sqrt{5} - 5\sqrt{3}$
Combine like terms.
Group the terms with $\sqrt{3}$ :
$(6\sqrt{3} - 5\sqrt{3}) + 5\sqrt{5}$ $(6-5)\sqrt{3} + 5\sqrt{5}$ $1\sqrt{3} + 5\sqrt{5}$ $\sqrt{3} + 5\sqrt{5}$

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