To simplify the expression 3√5 × 2√10, we can first simplify the square roots separately and then multiply the simplifications together.
1. Simplify √5:
The square root of 5 cannot be simplified any further because 5 is not a perfect square.
2. Simplify √10:
The square root of 10 can be simplified by expressing it as the product of the square root of its largest perfect square factor. The largest perfect square factor of 10 is 2:
√10 = √(2 × 5) = √2 × √5 = √2√5
3. Multiply the simplified square roots together:
Now that both square roots are simplified, we can multiply them together:
3√5 × 2√10 = 3(√5) × 2(√2√5) = 6(√(5 × 2 × 5)) = 6(√(50)) = 6√50
4. Simplify the final answer:
The square root of 50 can be simplified by expressing it as the product of the square root of its largest perfect square factor. The largest perfect square factor of 50 is 25:
6√50 = 6√(25 × 2) = 6(√25√2) = 6(5√2) = 30√2
Therefore, the simplified form of 3√5 × 2√10 is 30√2.
Show all of your steps for how to simplify 3√5×2√10
. Your final answer should be in simplified radical form (not a decimal).
1 answer