Question

What is the simplest form of the product?
SqRt 63x^5y^3 • sqRt 14xy8

Answer 1

`√(63x^5y^3)\cdot√(14xy^8)=√(63x^5y^3\cdot14xy^8)=\sqrt{63\cdot14\cdot x^(5+1)y^(3+8)}\\\\=\sqrt{9\cdot7\cdot7\cdot2\cdot x^6y^(11)}=\sqrt9\cdot√(7^2)\cdot√(2)\cdot√(x^6)\cdot\sqrt{y^(11)}\\\\=3\cdot7\cdot\sqrt2\cdot√((x^3)^2)\cdot\sqrt{y^(10)\cdot y}=21\sqrt2\cdot x^3\cdot√((y^5)^2)\cdot√(y)\\\\=21x^3y^5√(2y)`

Answer 2

`√(63x^5y^3) \cdot √( 14xy^8 )=\\ \\=√(63x^5y^3\cdot 14xy^8 )=\\ \\\sqrt{882x^(5+1) y^3 y^8 } =\\ \\=√(441 \cdot 2 \cdot x^6y^3y^8)=\\ \\=√(441) \cdot √(y^8)\cdot \sqrt{x^(6) }\cdot √(2y^3) = \\ \\=21 \cdot( y ^(8 ))^(1)/(2)\cdot ( x^6)^{(1)/(2)}*\sqrt{2y^(3)}\\ \\=21 \cdot x^3 \cdot y^4 \cdot √(2y^3)`