What is the simplified form of the expression \sqrt{50} - \sqrt{18} + \sqrt{8}? — JAMB UTME

What is the simplified form of the expression $\sqrt{50} - \sqrt{18} + \sqrt{8}$ ?

The simplified form of the expression is

4\sqrt{2}

Simplifying each radical into basic surd form yields

\sqrt{50} = 5\sqrt{2}

\sqrt{18} = 3\sqrt{2}

, and

\sqrt{8} = 2\sqrt{2}

. Combining these like terms gives

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

Simplify each surd term into basic surd form

\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}

\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}

, and

\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}

Converting each surd to have a common radicand allows for addition and subtraction of like terms.

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

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

Surds with identical radicands can be combined by operating on their coefficients.

Simplification and Addition/Subtraction of Like Surds

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