Final answer:
The expression 3√12×7√15 simplifies to 126√5.
Step-by-step explanation:
To simplify the mathematical expression 3√12×7√15, we first need to simplify the radicals (square roots). The square root of 12 can be simplified to 2√3, and the square root of 15 can be simplified to √15. Therefore, the expression becomes 3(2√3)×7√15, which simplifies to 6√3×7√15.
Next, we can multiply the numbers outside the radicals, which gives us 42√3√15. Finally, since we're multiplying radicals, we can combine them under one radical to get 42√45 (since 3×15 equals 45). The square root of 45 can further be simplified to √9×√5 or 3√5.
Therefore, our final simplified form is 42×3√5 = 126√5.
Learn more about Simplifying Radicals