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:

$3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6$

Step-by-step explanation:

To find the product :

$(\sqrt{3x} +\sqrt5)(\sqrt{15x} +2\sqrt{30})$

$\sqrt{3x}(\sqrt{15x} +2\sqrt{30}) +\sqrt5(\sqrt{15x} +2\sqrt{30})\\\Rightarrow \sqrt{3x}\times \sqrt{15x} +\sqrt{3x}\times 2\sqrt{30} +\sqrt5 \times \sqrt{15x} +\sqrt5\times 2\sqrt{30}\\\Rightarrow \sqrt{45} \times x + 2 \sqrt{90x} + \sqrt{75x} + 2 \sqrt{150}\\\Rightarrow \sqrt{5 \times 9} \times x + 2 \sqrt{9\times 10x} + \sqrt{25 \times 3x} + 2 \sqrt{25 \times 6}\\\Rightarrow 3\sqrt5 x+ 2 \times 3 \sqrt{10x} +5\sqrt{3x} +2 \times 5 \sqrt6\\\Rightarrow 3\sqrt5 x+ 6 \sqrt{10x} +5\sqrt{3x} +10 \sqrt6$

$\Rightarrow 3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6$

Some identities used:

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

2. $\sqrt9 =3$

3. $\sqrt{25} =5$

4. $\sqrt x \times \sqrt x=x$

5. $\sqrt a \times \sqrt b = \sqrt{ab}$

So, the solution is $3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6$

Answer 2

Answer:it’s b

Step-by-step explanation:

On edge