Question

Rikki says that the product square root of 3x5^3 x the square root of 5 is 3 x 5^2 , or 75. Explain rikki's error and write the correct product.

Answer 1

Rikki's mistake is treating √3 as 3 (or otherwise dropping the square root on the 3). You cannot remove the square root from 3.

Correct work:
√(3·5^3) · √5 = √[(3·5^3)·5] = √(3·5^4) = √3 · √(5^4) = √3 · 5^2 = 25√3.

Numerically 25√3 ≈ 43.30, not 75.