Question

Rationalize 2 divided by the square root of 7

Answer 1

`(2√(7))/(7)`

Explanation:

There's a radical in the denominator of the fraction

`(2)/(√(7))`.

Multiplying the denominator
`√(7)` by a certain number will get rid of its radical part. What number will serve the purpose? There's only one square root in the denominator, so multiplying the square root
`√(7)` by itself will do.

Multiple both the fraction by

`(√(7))/(√(7))`,

which is the same as multiplying by
`1`,

will rationalize the denominator without changing the value of the fraction. Here's how it works:

`\begin{array}{ll} (2)/(√(7))\\= (2)/(√(7)) * 1 & \text{Doing so does not change the value.}\\= (2)/(√(7)) * (√(7))/(√(7)) & \text{The value of} \; \frac{√(7)} {√(7)} \; \text{is} \; 1 \text{.} \\=(2√(7))/((√(7))^(2)) & \text{Square the square root} \; √(7)\text{.}\\= (2√(7))/(7)\\\end{array}`.