Question

I need helps plssssss. If you could explain that would be great!

Answer 1

`5√(15)`

Explanation:

`(√(3)+√(48))(√(20)-√(5))`

`\textsf{Use} \quad √(a)√(b)=√(ab)`

`\implies (√(3)+√(16 \cdot 3))(√(4 \cdot 5)-√(5))`

`\implies (√(3)+√(16)√(3))(√(4)√(5)-√(5))`

`\implies (√(3)+4√(3))(2√(5)-√(5))`

`\implies (5√(3))(√(5))`

`\implies 5√(3)√(5)`

`\implies 5√(3 \cdot 5)`

`\implies 5√(15)`

Answer 2

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