√6(√2+√3)

1 answer

To simplify this expression, we can use the distributive property of multiplication:

√6(√2+√3) = √6*√2 + √6*√3

Next, we can simplify each term under the radicals by recognizing that 6 can be factored into 2*3:

√6*√2 = √(2*3)*√2 = √6*√2*√2 = √12

Similarly, √6*√3 = √(2*3)*√3 = √6*√3*√3 = √18

Now we can substitute these simplified terms into our expression:

√6(√2+√3) = √12 + √18

We can simplify this further by factoring out the largest perfect square that is a factor of both 12 and 18, which is 36:

√12 + √18 = √(4*3)+√(9*2) = 2√3 + 3√2

Therefore, √6(√2+√3) = 2√3 + 3√2.