Question

@jim_thompson5910 What is the exact value of the expression 8the square root of 15. + 5the square root of 5. + the square root of 15.?

14 sqrt 35 ?

Answer 1

combine like terms

Answer 2

this is NOT a valid move

\[\large \sqrt{15}+\sqrt{15} = \sqrt{30}\]

that equation above is NOT true

Answer 3

so,

\[\large \sqrt{15}+\sqrt{15} \neq \sqrt{30}\]

Answer 4

Okay.

Answer 5

it might help to replace every sqrt(15) with x and sqrt(5) with y

Answer 6

that would turn

\[\large 8\sqrt{15} + 5\sqrt{5} + \sqrt{15}\]

into

\[\large 8x + 5y + x\]

Answer 7

13xy+x?

Answer 8

8x+5y cannot be combined to 13xy

Answer 9

x and y are unlike terms

Answer 10

but 8x and x are like terms

Answer 11

9x

Answer 12

so you now have 9x + y

Answer 13

that turns back into \[\large 9\sqrt{15} + \sqrt{5}\]

Answer 14

so,

\[\large 8\sqrt{15} + 5\sqrt{5} + \sqrt{15} = 9\sqrt{15} + \sqrt{5}\]

Answer 15

Oh, thanks again.

Answer 16

yw