Originally Posted by

**allyourbass2212** The book I am using me seems to contradict itself

**P**- Parenthesis First

**E**- Exponents and roots second

**M** - multiplication third from left to right

**D**- division third from left to right (do both multiplication and division together)

**A**-addition fourth

**S**-subtraction last

However if we are to abide by the order of operations stated above, the book seems to contradict itself in the following example

1. $\displaystyle \sqrt{\frac{4(10+6)}{10+3(5)}}$

**Parentheses** First:

$\displaystyle \sqrt{\frac{4(16)}{10+15}}$

**Exponents and ROOTS **second:Now here is where im lost. The whole expression in this case is underneath a root yet instead of taking the squared root of this whole expression the author precedes to add the numbers together to produce $\displaystyle \sqrt{\frac{64}{25}}$ and then ends simplifying the expression by considering the roots, no where near the second order in the operation $\displaystyle \sqrt{\frac{64}{25}}=\sqrt{\frac{8}{5}}$ as indicated by PEMDAS, instead of exponents/roots coming second it comes last in this case.