If \frac{\sqrt{50} + \sqrt{18}}{\sqrt{2}} = m, what is the value of the integer m? — JAMB UTME

If $\frac{\sqrt{50} + \sqrt{18}}{\sqrt{2}} = m$ , what is the value of the integer $m$ ?

Answer: 8

The value of the integer

m

is 8.

Simplifying

\sqrt{50}

5\sqrt{2}

and

\sqrt{18}

3\sqrt{2}

gives a numerator of

8\sqrt{2}

. Dividing

8\sqrt{2}

\sqrt{2}

cancels out the radical part, yielding the integer 8.

Simplify the radical expressions in the numerator.

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

and

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

Factor out perfect square numbers from within each radical.

Sum the simplified surds in the numerator.

5\sqrt{2} + 3\sqrt{2} = 8\sqrt{2}

Surds with identical radicands are like terms and can be added by adding their coefficients.

Divide the numerator by the denominator.

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

Cancel the common factor of

\sqrt{2}

present in both numerator and denominator.

Simplification and division of surds

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