Answer:
5√15
Explanation:
(√3 + √48)(√20 - √5)
step 1 simplify √48
(√3 + 4√3)(√20 - √5)
step 2 add √3 and 4√3
(5√3)(√20 - √5)
step 3 simplify √20
(5√3)(2√5 - √5)
step 4 subtract √5 from 2√5
(5√3)(√5)
step 5 multiply 5√3 and √5
= 5√15
explanation of each step
step 1 and 3
To simplify radicals you list the factors of the number under the sqaure root
For 48 we have 2 × 2 × 2 × 2 × 3
We then pair the factors off as powers of 2 if possible
We get 2² × 2² × 3 which can further be simplified as 4² × 3
We then list the number with the power on the outside of the radical and leave the numbers with no power on the inside to get 4√3.
This process is used to simplify √20 as well.
step 2 and 4
For these two steps we are adding and subtracting radicals with the same radicand ( number inside of the square root. ) This is very simply as we keep the radicand the same and just perform the operation to the coeffecients ( number on the outside of the square root )
Eg. a√b + c√b = (a+c)√b or a√b - c√b = (a-c)√b
Hence, 4√3 + √3 = (4+1)√3 = 5√3
Step 5.
Finally we multiply the two radicals. This is very simply as we can use the rule to do so.
a√b × c√d = (a×c)√b×d
Hence, 5√3 × √5 = (5×1)√(3×5) = 5√15