If the surd expression \frac{12}{\sqrt{6}} is simplified to the form k\sqrt{6}, what is th… — JAMB UTME

If the surd expression $\frac{12}{\sqrt{6}}$ is simplified to the form $k\sqrt{6}$ , what is the value of $k$ ?

Answer: 2

The value of

k

is 2.

Multiplying the numerator and denominator of

\frac{12}{\sqrt{6}}

\sqrt{6}

yields

\frac{12\sqrt{6}}{6}

. Dividing

12

6

simplifies the expression to

2\sqrt{6}

. Matching this with

k\sqrt{6}

gives

k = 2

Rationalize the denominator of

\frac{12}{\sqrt{6}}

by multiplying the numerator and denominator by

\sqrt{6}

\frac{12\sqrt{6}}{6}

Multiplying by

\frac{\sqrt{6}}{\sqrt{6}}

removes the radical from the denominator without changing the value of the expression.

Divide the integer coefficient in the numerator by the denominator.

2\sqrt{6}

Simplifying

\frac{12}{6}

yields 2.

Compare

2\sqrt{6}

with

k\sqrt{6}

to determine the value of

k

k = 2

The coefficient of

\sqrt{6}

is 2.

Rationalization of monomial surd denominators

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