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Simplify sqrt(75) - sqrt(48)

September 3, 2026Mathematics

ScanSolve AI Answer

Answer

\sqrt{3}

3 steps

here's how to solve the expression:

\sqrt{75} - \sqrt{48}

Simplify each radical by finding the largest perfect square factor.
$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$ $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$
Substitute the simplified radicals back into the expression.
$5\sqrt{3} - 4\sqrt{3}$
Combine the like terms by subtracting their coefficients.
$(5-4)\sqrt{3} = 1\sqrt{3} = \sqrt{3}$
The final answer is $\sqrt{3}$ .