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Rationalise the denominators, simplifying your answer where possible:
a)
(1)/(sqrt7)

Rationalise the denominators, simplifying your answer where possible: $\newline$ $\frac{1}{\sqrt{7}}$

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Simplify radical expressions using conjugates

Full solution

Q. Rationalise the denominators, simplifying your answer where possible:

\newline

\frac{1}{\sqrt{7}}

Identify conjugate of denominator: Identify the conjugate of the denominator $\sqrt{7}$ . $\newline$ The conjugate of $\sqrt{7}$ is $-\sqrt{7}$ . However, to rationalize, we use $\sqrt{7}$ itself to avoid changing the sign. $\newline$ Multiply the numerator and the denominator by $\sqrt{7}$ . $\newline$ $\frac{1 \times \sqrt{7}}{\sqrt{7} \times \sqrt{7}}$
Multiply by $\sqrt{7}$ : Perform the multiplication in the numerator and the denominator. $\newline$ Numerator: $1 \times \sqrt{7} = \sqrt{7}$ $\newline$ Denominator: $\sqrt{7} \times \sqrt{7} = 7$ $\newline$ The final expression is $\frac{\sqrt{7}}{7}.$

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