How do you simplify 4(sqrt2-sqrt7)?

1 Answer
George C.
Jul 3, 2017

4(sqrt(2)-sqrt(7)) = 4sqrt(2)-4sqrt(7)

Explanation:

The two square roots sqrt(2) and sqrt(7) are essentially unrelated to one another. So about all we can do to simplify the given expression is multiply it out to get:

4(sqrt(2)-sqrt(7)) = 4sqrt(2)-4sqrt(7)

color(white)()
Bonus

If you encountered 4(sqrt(2)-sqrt(7)) as the denominator of a rational expression, then you could rationalise the denominator by multiplying by sqrt(2)+sqrt(7). For example:

1/(4(sqrt(2)-sqrt(7))) = (sqrt(2)+sqrt(7))/(4(sqrt(2)-sqrt(7))(sqrt(2)+sqrt(7)))

color(white)(1/(4(sqrt(2)-sqrt(7)))) = (sqrt(2)+sqrt(7))/(4((sqrt(2))^2-(sqrt(7))^2))

color(white)(1/(4(sqrt(2)-sqrt(7)))) = (sqrt(2)+sqrt(7))/(4(2-7))

color(white)(1/(4(sqrt(2)-sqrt(7)))) = (sqrt(2)+sqrt(7))/(-20)

color(white)(1/(4(sqrt(2)-sqrt(7)))) = -sqrt(2)/20-sqrt(7)/20

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