To multiply √5 by √10, we multiply the numbers outside (√5 and √10) and also multiply the numbers inside (5 and 10):
√5 * √10 = (√5)(√10) = √(5 * 10) = √50
To simplify √50, we can break it down into the product of two numbers where one of the numbers is a perfect square:
√50 = √(25 * 2) = √25 * √2 = 5√2
Therefore, 3√5 * 2√10 can be simplified to:
3√5 * 2√10 = 3 * 2 * √5 * √10 = 6 * √(5 * 10) = 6 * √50 = 6 * 5√2 = 30√2
3sqrt5 multiply 2sqrt10
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