can someone show me step by step how to do this radical expression?

Question

-2√3+5√27-4√45

Johnny Handsome is correct

Answer 1

Remember that a product inside a radical can be written as the product of two radicals.

Example: √(AxB) = √(A) x √(B)

So you can simplify the larger roots in the expression
√27 = √(9x3) = √9 x √3 = 3 x √3
√45 = √(9x5) = √9 x √5 = 3 x √5

Plug those in.
-2√3 + 5x(3x√3) - 4x(3x√5)

Simplify
-2√3 + 15√3 -12√5
13√3 - 12√5

And that cannot be simplified any more so your answer is
13√3 -12√5

(Edited because I'm an idiot and added instead of multiplied.)

Answer 2

Simplify -2√3 + 5√27 - 4√45.

-2√3 + 5√(3*9) - 4√(5*9) = -2√3 + 5*3√3 - 4*3√5
= -2√3 + 15√3 - 12√5 = 13√3 - 12√5

Answer 3

in mathematics, we have this rule of precedence on which to equate first if there are multiple signs in an equation. this is the MDAS which means multiplication first, then division then addition and lastly, subtraction.
so in your equation, group the numbers first..
-(2√3)+(5√27)-(4√45) = ?
first we have to extract the roots to simplify the equation...
√27 = √(3*3*3) right?
= 3√3 that's it; and
√45 = √(3*3*3*5)
= 3 √(3*5)
= 3 √15 it's simplified now

going back to the first equation:
-(2√3)+(5√27)-(4√45) = -(2√3)+(5*3√3)-(4*3√15)
= -(2√3)+(15√3)-(12√15)
= -17√3 - 12√15
that's the final answer.,..:)

Answer 4

exactly what is it that your instructor wants you to do?

do you want to simplify it?

pull out the sqrt(3) from each term....

note that sqrt(27) = sqrt (3 x 9) = sqrt (3) x sqrt(9) = sqrt(3) x 3

likewise sqrt(45) = sqrt(15) x sqrt(3)

making your equation...

-2 x sqrt(3) + 5 x sqrt(3) x 3 - 4 x sqrt(15) x sqrt (3)

which gives

sqrt(3) x ( -2 + 15 -4 x sqrt(15))

or

sqrt(3) x (13 - 4 x sqrt(15))

now. had the last term been 48 instead of 45, that would have made a lot more sense. giving

-2 x sqrt(3) + 5 x sqrt(3) x 3 - 4 x sqrt(16) x sqrt (3)

=

sqrt(3) x (-2 +15 -16) = -3 x sqrt(3)

are you sure you copied this correctly?

Answer 5

-2√3+5√27-4√45
-2√3+5√(9x3)-4√(9x5)
-2√3+15√3-36√5
13√3-36√5

thats right for sure...step by step

Answer 6

PEMDAS. The radicals are done at the same time as exponents. So, moving left to right, calculate the value of the radicals first. Then, multiply each value by the corresponding coefficient (-2 * sqr(3), etc). Then do simple addition/subtraction.

Answer 7

I see that 5 people (above me) have worked this out to an answer.

Two got the same answer and they're close, but they're wrong.

One simply got the wrong answer.

One got the right answer except that he messed up the parentheses in his answer.

One got the right answer.

Hope you can figure out which one is right.

Answer 8

a million) ? m ^10 = m^(10/2) = m^5 2) c ^ 4/3 = c*c^(a million/3) = c cuberoot(c) 3) ^3 ? j ^ 15 = j^(15/3) = j^5 4) 2 ? 25 v ^2 = 2(25v^2)^(a million/2) = 2(5v)^(2/2) = 2(5v) = 10v 5) -4* ^3? 27k^6 i think of you recommend -4 situations cuberoot of (27k^6) = -4 *(27k^6)^(a million/3) = -4 *(3k^2)^(3/3) = -4 *(3k^2) = -12k^2

Answer 9

SDMC and desiroo are wrong.

27 = 3*3*3
45 = 3*3*3*5
so
sqrt(27) = sqrt(3*3*3) = 3*sqrt(3)
and
sqrt(45) = sqrt(3*3*3*5) = 3*sqrt(3*5) = 3*sqrt(5)*sqrt(3)
-2sqrt(3)+5sqrt(27)-4sqrt(45)=
-2sqrt(3)+5*3*sqrt(3)-4*3*sqrt(5)*sqrt(3) =
sqrt(3)*(-2+5*3-4*3*sqrt(5))=
sqrt(3)*(13-12*sqrt(5))

Answer 10

-2sqrt(3) + 5sqrt(3)sqrt(9) - 4sqrt(5)sqrt(9)
-2sqrt(3) + 5*3*sqrt(3) - 4*3*sqrt(5)
13sqrt(3) - 12sqrt(5)