Are each of the statements below true or false? Explain your answer without just saying true or false.

o √a + √b = √(a + b) Explain why.

o The numerator and denominator of the following must be multiplied by √3 to rationalize 3/(3 + √3). Explain why.

Question

Are each of the statements below true or false?  Explain your answer without just saying true or false.

o    √a + √b = √(a + b)     Explain why.

o    The numerator and denominator of the following must be multiplied by √3 to rationalize 3/(3 + √3). Explain why.

myininaya · Answer

$$\sqrt{a}+\sqrt{b} \neq \sqrt{a+b}$$

moongazer · Answer

false, because √(a + b) means that you should add first a and b before having it √.
unlike in √a + √b you will only add the √ of a and b

myininaya · Answer

counterexample: if a=9 and b=25, then
$$\sqrt{9}+\sqrt{25}=3+5=8 \neq \sqrt{34}=\sqrt{9+25}$$

myininaya · Answer

second one: you must multiply the fraction by

myininaya · Answer

$$\frac{3-\sqrt3}{3-\sqrt3}$$

anonymous · Answer

myininaya so the second one is false too right

myininaya · Answer

yes it is false you change the value of that fraction when you multiply by square root of 3
you need to multiply by 
$$1=\frac{3-\sqrt{3}}{3-\sqrt{3}}$$

anonymous · Answer

myininaya thank you very much

myininaya · Answer

np