Question

Find the simplified product: 2√5x3(-3√10x2​

Answer 1

The simplified product of 2√5 and 3(-3√10) is calculated by multiplying integers and square roots separately, resulting in -90√2 after simplification.

Step-by-step explanation:

To find the simplified product of 2√5 and 3(-3√10), we multiply each term separately, respecting the rules for multiplying square roots and integers.

Step-by-Step Solution:

1. Multiply the integer parts: 2 * 3 * (-3) = -18.
2. Multiply the square root parts: √5 * √10 = √(5*10) = √50.
3. Combine the multiplications: -18 * √50 = -18√50.
4. Simplify the square root of 50, which can be expressed as √(25*2) = √25 * √2 = 5√2.
5. Now, we get the final result: -18 * 5√2 = -90√2.

Thus, the simplified product is -90√2.