Question

What is the product? Assume x greater-than-or-equal-to 0 (StartRoot 3 x EndRoot + StartRoot 5 EndRoot) (StartRoot 15 x EndRoot + 2 StartRoot 30 EndRoot)

Answer 1

Answer:it’s b

Explanation:

On edge

Answer 2

`3\sqrt5 x+ \sqrt x (6 √(10) +5√(3)) +10 \sqrt6`

Explanation:

To find the product :

`(√(3x) +\sqrt5)(√(15x) +2√(30))`

`√(3x)(√(15x) +2√(30)) +\sqrt5(√(15x) +2√(30))\\\Rightarrow √(3x)* √(15x) +√(3x)* 2√(30) +\sqrt5 * √(15x) +\sqrt5* 2√(30)\\\Rightarrow √(45) * x + 2 √(90x) + √(75x) + 2 √(150)\\\Rightarrow √(5 * 9) * x + 2 √(9* 10x) + √(25 * 3x) + 2 √(25 * 6)\\\Rightarrow 3\sqrt5 x+ 2 * 3 √(10x) +5√(3x) +2 * 5 \sqrt6\\\Rightarrow 3\sqrt5 x+ 6 √(10x) +5√(3x) +10 \sqrt6`

`\Rightarrow 3\sqrt5 x+ \sqrt x (6 √(10) +5√(3)) +10 \sqrt6`

Some identities used:

1.
`(a+b)(c+d) = a (c+d) + b(c+d)`

2.
`\sqrt9 =3`

3.
`√(25) =5`

4.
`\sqrt x * \sqrt x=x`

5.
`\sqrt a * \sqrt b = √(ab)`

So, the solution is
`3\sqrt5 x+ \sqrt x (6 √(10) +5√(3)) +10 \sqrt6`