To simplify 4â45 you will think to think of two numbers that when multiplied together give 45 and one of those numbers needs to be a perfect square (a number that can be square rooted and leave no remainder/decimals):
â9 x 5â5
= 3 x 5â5
= 15â5
Now to simplify â80 you will need to think of two numbers that when multiplied together give 80 and one of those numbers needs to a perfect square:
â16 x â5
= 4 x â5
= 4â5
Notice that now that we have simplified the radicals we have a common base and can add them together!
Answers & Comments
Verified answer
5√45+√80
5√45=5√(9*5)=5*3√5=15√5
√80=√(16*5)=4√5
15√5+4√5=19√5
5â45 + â80
= 5â(9 x 5) + â(16 x 5)
= (5 x 3)â5 + 4â5
= 15â5 + 4â5
= 19â5
To simplify 4â45 you will think to think of two numbers that when multiplied together give 45 and one of those numbers needs to be a perfect square (a number that can be square rooted and leave no remainder/decimals):
â9 x 5â5
= 3 x 5â5
= 15â5
Now to simplify â80 you will need to think of two numbers that when multiplied together give 80 and one of those numbers needs to a perfect square:
â16 x â5
= 4 x â5
= 4â5
Notice that now that we have simplified the radicals we have a common base and can add them together!
15â5 + 4â5 = 19â5
Convert these into mixed radical form first.
5â(9x5) + â(16x5)
Then take out your perfest square...
5(3)â5 + 4â5
Simplify outside the square root sign.
15â5 + 4â5
Add only the coefficiants, not what's under the square root!
19â5
So your final answer is 19â5. :)
5 sqrt(45) + sqrt(80)
= 5 sqrt(3*3*5) + sqrt(2*2*2*2*5)
= 5*3*sqrt(5) + 2*2*sqrt(5)
= 15 sqrt(5) + 4 sqrt(5)
= 19 sqrt(5)
42.48529157