# Find the Distance Between Two Points (5 square root of 3, square root of 2) , (- square root of 3, square root of 2)

(53,2) , (-3,2)
Use the distance formula to determine the distance between the two points.
Distance=(x2-x1)2+(y2-y1)2
Substitute the actual values of the points into the distance formula.
((-3)-53)2+(2-2)2
Simplify.
Subtract 53 from -3.
(-63)2+(2-2)2
Simplify the expression.
Apply the product rule to -63.
(-6)232+(2-2)2
Raise -6 to the power of 2.
3632+(2-2)2
3632+(2-2)2
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
36(312)2+(2-2)2
Apply the power rule and multiply exponents, (am)n=amn.
36⋅312⋅2+(2-2)2
Combine 12 and 2.
36⋅322+(2-2)2
Cancel the common factor of 2.
Cancel the common factor.
36⋅322+(2-2)2
Divide 1 by 1.
36⋅31+(2-2)2
36⋅31+(2-2)2
Evaluate the exponent.
36⋅3+(2-2)2
36⋅3+(2-2)2
Multiply 36 by 3.
108+(2-2)2
Subtract 2 from 2.
108+02
Simplify the expression.
Raising 0 to any positive power yields 0.
108+0
108
108
Rewrite 108 as 62⋅3.
Factor 36 out of 108.
36(3)
Rewrite 36 as 62.
62⋅3
62⋅3
Pull terms out from under the radical.
63
63
The result can be shown in multiple forms.
Exact Form:
63
Decimal Form:
10.39230484…
Find the Distance Between Two Points (5 square root of 3, square root of 2) , (- square root of 3, square root of 2)

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