GB-39-05-001 · Rationalising a binomial

Rationalise the denominator and simplify $\frac{1281}{14-\sqrt{13}}$ .

Surds: Rationalising the Denominator (2 Terms / Conjugate) Booklet p. 48

Method

1) Swap sign in denominator to get the conjugate (a + √p)

2) Multiply top and bottom by conjugate (use 2×2 grid for denominator)

3) Simplify fraction

Worked Example (GB-39-05-001)

Booklet p. 48: Swap sign in denominator to get conjugate

(14 + \sqrt{13})

and multiply top & bottom:

Numerator:

1281(14 + \sqrt{13})

Divide by denominator

183

\frac{1281}{183}(14 + \sqrt{13}) = 7(14 + \sqrt{13})

Denominator Grid:

196 - 13 = 183

×	$14$	$-\sqrt{13}$
$14$	$196$	$-14\sqrt{13}$
$+\sqrt{13}$	$+14\sqrt{13}$	$-13$

98+7\sqrt{13}