Question

What is the following product? (2 square root 7+3 square root 6)(5 square root 2+4 square root 3)

Answer 1

`(2\sqrt7+3\sqrt6)(5\sqrt2+4\sqrt3)\qquad\text{use distributive property}\\\\=(2\sqrt7)(5\sqrt2)+(2\sqrt7)(4\sqrt3)+(3\sqrt6)(5\sqrt2)+(3\sqrt6)(4\sqrt3)\\\\=10√(14)+8√(21)+15√(12)+12√(18)\\\\=10√(14)+8√(21)+15√(4\cdot3)+12√(9\cdot2)\\\\=10√(14)+8√(21)+15\sqrt4\cdot\sqrt3+12\sqrt9\cdot\sqrt2\\\\=10√(14)+8√(21)+(15)(2)\sqrt3+(12)(3)\sqrt2\\\\=\boxed{10√(14)+8√(21)+30\sqrt3+36\sqrt2}`

Answer 2

Answer: The required product is
`10√(14)+8√(21)+30\sqrt3+36\sqrt2.`

Step-by-step explanation: We are given to find the following product :

P = (2 square root 7+3 square root 6)(5 square root 2+4 square root 3).

We will be using the following property of radicals :

`\sqrt a* \sqrt b=√(ab).`

The given product can be written and evaluated as follows :

`P\\\\=(2\sqrt7+3\sqrt6)(5\sqrt2+4\sqrt3)\\\\=2\sqrt7(5\sqrt2+4\sqrt3)+3\sqrt6(5\sqrt2+4\sqrt3)\\\\=10√(7*2)+8√(7*3)+15√(6*2)+12√(6*3)\\\\=10√(14)+8√(21)+15*2*\sqrt3+12*3\sqrt2\\\\=10√(14)+8√(21)+30\sqrt3+36\sqrt2.`

Thus, the required product is
`10√(14)+8√(21)+30\sqrt3+36\sqrt2.`