Question

If t{8} -8\sqrt{18} = \sqrt{n}" alt="18\sqrt{8} -8\sqrt{18} = \sqrt{n}" align="absmiddle" class="latex-formula">, what is $n$?

Answer 1

I believe the answer is N=288

Answer 2

Answer:

n = 288

Step-by-step explanation:

18 sqrt(8) - 8 sqrt(18) = sqrt(n)

18 sqrt(4*2) - 8 sqrt(9*2) = sqrt(n)

We know that sqrt(ab) = sqrt(a) sqrt(b)

18 sqrt(4) sqrt(2) - 8 sqrt(9) sqrt(2) = sqrt(n)

18*2 sqrt(2) - 8*3 sqrt(2) = sqrt(n)

36 sqrt(2) - 24 sqrt(2) = sqrt(n)

12 sqrt(2) = sqrt(n)

Square each side

(12 sqrt(2))^2 = (sqrt(n))^2

12^2*(sqrt(2))^2 = n

144 *2 =n

288 =n