simply. assume all variables represent positive real numbers (sqrt = quare root): 1.) sqrt. 96x^2 y
2.) ^4 sqrt. 16a^4
3.) ^3 sqrt. 64x^4 y^5

Question

simply. assume all variables represent positive real numbers (sqrt = quare root): 1.) sqrt. 96x^2 y
2.) ^4 sqrt. 16a^4    
3.) ^3 sqrt. 64x^4 y^5

anonymous · Answer

please help, i am taking an exam & dont understand it :(

anonymous · Answer

i dont understand what you are supposed to find out.

anonymous · Answer

like whats it on? on my exam it just says to simplify

anonymous · Answer

its 3 different problems

anonymous · Answer

$$\sqrt{96x ^{2}y}=\sqrt{16*6x ^{2}y}=4x \sqrt{6y}$$

anonymous · Answer

$$\sqrt[4]{16a ^{4}}=\sqrt[4]{(2a)^{4}} = 2a$$

anonymous · Answer

$$\sqrt[3]{64 x ^{4}y ^{5}}=\sqrt[3]{(4xy)^{3}xy ^{2}}=4xy \sqrt[3]{xy ^{2}}$$

anonymous · Answer

THANK YOU SO MUCH !

anonymous · Answer

can you help me out please with a couple more problems?

anonymous · Answer

no, I can't do your problems for you. I have shown you how to do these problems. You can do the rest on your own if you apply the same logic. if you have doubts, feel free to ask and I will clarify.

anonymous · Answer

aw okay , thanks though. but for adding and subtracting them with others would they need the same sqrt inside ?

anonymous · Answer

give me an example.

anonymous · Answer

[2 sqrt. 128] + [5 sqrt. 32] + [2 sqrt.200]

anonymous · Answer

sqrt3 is a number. So if you had 3sqrt 3 +5sqrt3 sqrt 4, you can factor out sqrt3 as if it was a number so it would become sqrt 3 (3+5sqrt4)

anonymous · Answer

you mean [2 sqrt.200] as sqrt.3 ?

anonymous · Answer

no , I was giving an example of my own. In your problem you can express sqrt 200 as sqrt 8 sqrt 25. you can express sqrt 32 as sqrt4 sqrt 8. you can express sqrt 128 as sqrt 8 sqrt 16

anonymous · Answer

how do you know how to express it ?

anonymous · Answer

you see what is the highest common factor between 200, 32 and 128 and factor it out.

anonymous · Answer

all 3 have to have the same in common ?

anonymous · Answer

which would be 8 ?

anonymous · Answer

yup.

anonymous · Answer

so answer would be 9 sqrt.8 ?

anonymous · Answer

the numbers add up to 9

anonymous · Answer

nope.

anonymous · Answer

2 + 5 + 2 = 9 ?

anonymous · Answer

it does

anonymous · Answer

so if we have the same sqrt. already than just add the numbers which give 9

anonymous · Answer

yes, but 2 sqrt 200 = 2 sqrt 5 sqrt 8 = 2*5 sqrt 8= 10sqrt8

anonymous · Answer

sorry 2*sqrt 200 = 2*sqrt 25*sqrt 8 = 2*5*sqrt8 = 10sqrt8

anonymous · Answer

and simplfying that would give [2 sqrt. 2] ?

anonymous · Answer

half of each other

anonymous · Answer

yes, if you want to simply it further, sqrt 8 = 2 sqrt2

anonymous · Answer

and to simplfy that is 1 ?

anonymous · Answer

simplify what is 1?