Question

simplify this radical

Answer 1

\[4\sqrt{128} +5\sqrt{18}\]

Answer 2

sorry it took a while

Answer 3

first, can you factorise 128 into a product of prime numbers?

Answer 4

like 8 or 16? sorry bad with prime numbers

Answer 5

you could start like this
128 = 2 * 64
[pulling out one prime factor]

then factorise 64

Answer 6

ok so when i factorize 64 i get 12 or

Answer 7

wait im working it out hehe sorry

Answer 8

64 = a * b

what could a and b be?

Answer 9

18

Answer 10

wait no let me work it out

Answer 11

im sorry im confused

Answer 12

64 is an even number right?

Answer 13

wait if 64 is a perfect square of 8 can that be it?

Answer 14

yes it is an even number

Answer 15

yeah you can say 64 = 8 * 8

Answer 16

ok so how will i be able to solve the radical using 8

Answer 17

you have
128 = 2 * 64
= 2 * 8 * 8
= 2 * 8^2

Answer 18

oh

Answer 19

so

√128 = √(2 * 8^2)
=

Answer 20

the square root of a product equals the product of square roots
√(2 * 8^2) = √2 * √(8^2)

Answer 21

and the square root of a square number, equals the number
√x^2 = x

Answer 22

so then its like \[4\sqrt{8^2}\]

Answer 23

4 * √128 = 4 * √ 2 * √8^2 (dont forget the √2)

Answer 24

oh ya

Answer 25

now simplify the √8^2 term

Answer 26

well by doing the exponent you get 64 again

Answer 27

though if you want to put it down to its smallest number its 8 and 8^2 is 4 when simplified i think

Answer 28

to simplify √8^2

use √x^2 = x

Answer 29

oh ok i think i get it

Answer 30

so

4 * √128 = 4 * √ 2 * √8^2
= 4 * √2 * ?

Answer 31

i thin\[9\sqrt{18}\]k you will get

Answer 32

i think i will get

Answer 33

how?

Answer 34

well if you add the 4+5 you get 9 and when you solve through the steps isnt the 128 suppose to be simplified into an 18 im still not sure though

Answer 35

128 ≠ 18