2radical10(radical5 +3radical2)
To simplify the expression 2√10 (√5 + 3√2), we need to apply the distributive property.
First, we distribute 2√10 to both terms inside the parentheses:
2√10 * √5 = 2√(10 * 5) = 2√50
2√10 * 3√2 = 6√(10 * 2) = 6√20
Now we have:
2√10 (√5 + 3√2) = 2√50 + 6√20
Next, we can simplify the radicals further.
√50 can be simplified as follows:
√50 = √(25 * 2) = √25 * √2 = 5√2
Similarly, √20 can be simplified as:
√20 = √(4 * 5) = √4 * √5 = 2√5
Substituting these simplified radicals back into the expression, we get:
2√10 (√5 + 3√2) = 2(5√2) + 6(2√5) = 10√2 + 12√5
So, the simplified form of 2√10 (√5 + 3√2) is 10√2 + 12√5.