Question

Multiply if possible and simplify
`\sqrt{50x^(7)y^(7) }`·
`\sqrt{6xy^(4) }`

Answer 1

`\large\boxed{(\sqrt{50x^(7)y^(7) })(\sqrt{6xy^(4) })=\sqrt{300x^8y^(11)}=10x^4y^5√(3y)}`

Explanation:

`\text{Use}\ √(ab)=√(a)\cdot√(b)\\\\(\sqrt{50x^(7)y^(7) })(\sqrt{6xy^(4) })=√((50x^7y^7)(6xy^4))=√((50\cdot6)(x^7x)(y^7y^4))\\\\\text{Use}\ a^na^m=a^(n+m)\\\\=\sqrt{300x^(7+1)y^(7+4)}=\boxed{\sqrt{300x^8y^(11)}}\\\\\text{Use}\ (a^n)^m=a^(nm)\ \text{and}\ a^n\cdot a^m=a^(n+m)\\\\=\sqrt{(100\cdot3)x^(4\cdot2)y^(5\cdot2+1)}=√((100\cdot3)(x^4)^2(y^5)^2y)\\\\\text{Use}\ √(ab)=√(a)\cdot√(b)\ \text{and}\ √(a^2)=a`

`=√(100)\cdot√((x^4)^2)\cdot√((y^5)^2)\cdot√(3y)=\boxed{10x^4y^5√(3y)}`