# How do you simplify -5/(2sqrt112)?

Aug 6, 2016

$\frac{- 5 \sqrt{7}}{56}$

#### Explanation:

$- \frac{5}{2 \sqrt{112}}$

Rationalise the denominator:
(-5sqrt(112))/(2sqrt(112)sqrt(112) $= \frac{- 5 \sqrt{112}}{2 \cdot 112}$

Express the $\sqrt{112}$ as the root of the product of prime numbers:

$= \frac{- 5 \cdot \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 7}}{224}$

Each pair of primes may be taken out of the sqrt

$= \frac{- 5 \cdot 2 \cdot 2 \sqrt{7}}{224}$

$= \frac{- 5 \sqrt{7}}{56}$