Question

`√(3) \cdot √(6) \cdot √(10) \cdot (√(5))^3`

Answer 1

The answer to this problem would be 150

Answer 2

150

Explanation:

Given expression:

`√(3) \cdot √(6) \cdot √(10) \cdot (√(5))^3`

Expand the brackets:

`\implies √(3) \cdot √(6) \cdot √(10) \cdot √(5) \cdot √(5) \cdot √(5)`

`\textsf{Apply radical rule} \quad √(a)√(b)=√(ab)`

`\implies √(3 \cdot 6 \cdot 10 \cdot 5 \cdot 5 \cdot 5)`

Multiply the numbers:

`\implies √(22500)`

Rewrite 22500 a 150²:

`\implies √(150^2)`

`\textsf{Apply radical rule} \quad √(a^2)=a, \quad a \geq 0`

`\implies 150`