Why is the answer to this maths question "18+ 12√2"?

18 + 4√18

can be simplified. Factor out a square from the 18 (the 9), so you get:

18 + 4√(9 * 2)
18 + 4√9 √2
18 + 4(3)√2
18 + 12√2

( √6 + 2 √ 3 ) ( √6 + 2 √ 3 )

6 + 2 √18 + 2 √18 + 12

18 + 4 √18

18 + (4) 3 √2

18 + 12 √2

it is always most correct to express square roots in their simplest terms.

sqrt(18) = Sqrt(9 x 2) = sqrt(3^2 x 2) = 3xSqrt(2)

btw, 12√2 is equal to 4√18, it is just more correct to express it as 12√2

18+ 12√2 and 18+4√18 are equal...

18 + 4√18
18 + 4√9√2
18 + 4(3)√2
18 + 12√2

So you're technically right, but 18 + 12√2 is just more simplified.

Hope I helped.

(√6 + 2√3)^2
= (√6 + 2√3)(√6 + 2√3)
= √(6 * 6) + 2√(3 * 6) + 2√(6 * 3) + (2 * 2)√(3 * 3)
= 6 + 2√18 + 2√18 + 4(3)
= 6 + 4√18 + 12
= 18 + 4√18