Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

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