Question

Find the distance between the points (6,5√5) and (4,3√2).
2, 2√2, 2√3

Answer 1

2 square of 3 is the answer

step-by-step explanation :

`\sqrt({x} _(2) - x_(1))^(2) + (y_(2) - y_(1))^(2) \\\\\sqrt({4} - 6})^(2) + (3√(2) - 5√(2) )^(2) \\\\= \sqrt(-2})^(2) + (-2√(2) )^(2) \\\\\\= \sqrt4 + 8 \\\\\\\\\\= \sqrt12 \\\\\\\\= 2√(3)`

Answer 2

D=
`\sqrt{(147-30√(10)}`

Explanation:

Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance

The distance formula is given as

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Here we are given two coordinates as

`(6,5√(5) ) , (4,3√(2) )`

Substituting these values in the Distance formula given above we get

`D=\sqrt{(6-4)^2+(5√(5) -3√(2)) ^2}`

`D=\sqrt{(2)^2+(5√(5))^2+(3√(2))^2-2*5√(5)*3√(2)}\\`

`D=\sqrt{4+125+18-2*15√(10)}\\D=\sqrt{147-30√(10)}\\`

Hence this is our answer