Question

Simplify √ 125 x 4 y 7 to the form a √ b .

Answer 1

`\large\boxed{5x^2y^3√(5y)}`

Explanation:

`√(125x^4y^7)=\sqrt{25\cdot5\cdot x^(2+2)\cdot y^(2+2+2+1)}\\\\\text{use}\ a^n\cdot a^m=a^(n+m)}\\\\=√(25\cdot5\cdot x^2\cdot x^2\cdot y^2\cdot y^2\cdot y^2\cdot y^1)\\\\\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=√(25)\cdot\sqrt5\cdot√(x^2)\cdot√(x^2)\cdot√(y^2)\cdot√(y^2)\cdot√(y^2)\cdot√(y)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=5\cdot\sqrt5\cdot x\cdot x\cdot y\cdot y\cdot y\cdot√(y)\\\\=5x^2y^3√(5y)`