Question

(2sqrt7+3sqrt6)(5sqrt2+4sqrt3)=

Answer 1

`10 \sqrt { 14 } + 8 \sqrt { 21 } + 30 \sqrt { 3 } + 36 \sqrt { 2 }`

Explanation:

We are given the following expression and we are to evaluate it:

`(2 \sqrt 7 + 3 \sqrt 6 ) ( 5 \sqrt 2 + 4 \sqrt 3 )`

Expanding this expression by multiplying each term with the rest of the terms to get:

`( 2 \sqrt { 7 } ) ( 5 \sqrt { 2 } + 4 \sqrt { 3 } ) + 3 \sqrt { 6 } ( 5 \sqrt { 2 } + 4 \sqrt { 3 } )`

Further simplifying it to get:

`10 \sqrt { 14 } ) + 8 \sqrt { 21 } ) + 15 \sqrt { 12 } + 12 \sqrt { 18 } )`

`10 \sqrt { 14 } + 8 \sqrt { 21 } + 30 \sqrt { 3 } + 36 \sqrt { 2 }`

Answer 2

`10√(14))+8√(21))+30√(3)+36√(2))`

Explanation:

The given product is:

`(2√(7)+3√(6))(5√(2)+4√(3))`

We expand using the distributive property to get;

`(2√(7))(5√(2)+4√(3))+3√(6)(5√(2)+4√(3))`

Simplify:

`=10√(14))+8√(21))+15√(12)+12√(18))`

`=10√(14))+8√(21))+30√(3)+36√(2))`