Question

Simplify: 5 the square root of 3 (2 the square root of 3 + 6 the square root of 19) Last one @jim_thompson5910

Answer 1

\[5\sqrt{3} (2\sqrt{3} + 6\sqrt{19})\]

Answer 2

step 1 is to distribute

Answer 3

What number? 5?

Answer 4

the whole number \(\large 5\sqrt{3}\)

Answer 5

you multiply that by EVERY term inside the parenthesis

so you're multiplying \(\large 5\sqrt{3}\) and \(\large 2\sqrt{3}\)

then

you're multiplying \(\large 5\sqrt{3}\) and \(\large 6\sqrt{19}\)

Answer 6

after all this, you add them together (combine like terms if possible, if not, then just leave it alone)

Answer 7

10 sqrt(9) and 30 sqrt(57)

Answer 8

Thank you.

Answer 9

now you can simplify things a bit, so you're not completely done

Answer 10

what is the square root of 9?

Answer 11

3

Answer 12

so 10*sqrt(9) = 10*3 = 30

Answer 13

which means the final answer is

\[\large 30 + 30\sqrt{57}\]