√6(√2+√3)
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.
To simplify the expression √6(√2 + √3), we can first distribute the square root of 6 to both terms inside the parentheses:
√6 * √2 + √6 * √3
Next, simplify each term separately:
√(6*2) + √(6*3)
√12 + √18
Now, we can simplify the square roots individually:
√(4*3) + √(9*2)
2√3 + 3√2
So, √6(√2 + √3) simplifies to 2√3 + 3√2.