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.
√6(√2+√3)
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