Question

What is the following product? assume y is greater than or less than 0

3sqrt10(y^2sqrt4+sqrt8y)
a.6y^2sqrt10+12sqrt5y
b.6sqrt10+12sqrt5y
c.6y^2sqrt10+4sqrt5y
d.3y^2sqrt10+12sqrt5y

Answer 1

Answer is A on Edge

Explanation:

Answer 2

`3√(10)(y^2\sqrt4+√(8y))\\\\\text{Use distributive law: a(b+c)=ab+ac, and we know}\ \sqrt4=2\\\\=3√(10)\cdot2y^2+3√(10)\cdot√(8y)\\\\\text{Use}\ √(a\cdot b)=√(a)\cdot√(b)\\\\=6y^2√(10)+3√(10\cdot8y)=6y^2√(10)+3√(80y)=6y^2√(10)+3√(16\cdot5y)\\\\=6y^2√(10)+3√(16)\cdot√(5y)\\\\\text{we know}\ √(16)=4\\\\=6y^2√(10)+3\cdot4√(5y)=\boxed{6y^2√(10)+12√(5y)\to a.}`