What is the simplified form of the surd expression \sqrt{45} - \sqrt{20} + \sqrt{80}? — JAMB UTME

What is the simplified form of the surd expression $\sqrt{45} - \sqrt{20} + \sqrt{80}$ ?

The simplified form of the expression is

5\sqrt{5}

Each radical is decomposed into a product involving a perfect square:

\sqrt{45} = 3\sqrt{5}

\sqrt{20} = 2\sqrt{5}

, and

\sqrt{80} = 4\sqrt{5}

. Combining the coefficients

(3 - 2 + 4)\sqrt{5}

yields

5\sqrt{5}

Simplify each individual surd into basic radical form by finding perfect square factors.

\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}

\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}

, and

\sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}

Expressing surds in terms of identical basic radicals allows like terms to be combined.

Substitute the simplified surds back into the original expression and combine like terms.

3\sqrt{5} - 2\sqrt{5} + 4\sqrt{5} = (3 - 2 + 4)\sqrt{5} = 5\sqrt{5}

Perform addition and subtraction on the coefficients of similar surds.

Simplification of Surds

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