# Find the Distance Between Two Points (3 square root of 7,-3 square root of 5) , (9 square root of 7,7 square root of 5)

(37,-35) , (97,75)
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.
(97-37)2+(75-(-35))2
Simplify.
Subtract 37 from 97.
(67)2+(75-(-35))2
Simplify the expression.
Apply the product rule to 67.
6272+(75-(-35))2
Raise 6 to the power of 2.
3672+(75-(-35))2
3672+(75-(-35))2
Rewrite 72 as 7.
Use axn=axn to rewrite 7 as 712.
36(712)2+(75-(-35))2
Apply the power rule and multiply exponents, (am)n=amn.
36⋅712⋅2+(75-(-35))2
Combine 12 and 2.
36⋅722+(75-(-35))2
Cancel the common factor of 2.
Cancel the common factor.
36⋅722+(75-(-35))2
Divide 1 by 1.
36⋅71+(75-(-35))2
36⋅71+(75-(-35))2
Evaluate the exponent.
36⋅7+(75-(-35))2
36⋅7+(75-(-35))2
Multiply.
Multiply 36 by 7.
252+(75-(-35))2
Multiply -3 by -1.
252+(75+35)2
252+(75+35)2
252+(105)2
Simplify the expression.
Apply the product rule to 105.
252+10252
Raise 10 to the power of 2.
252+10052
252+10052
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
252+100(512)2
Apply the power rule and multiply exponents, (am)n=amn.
252+100⋅512⋅2
Combine 12 and 2.
252+100⋅522
Cancel the common factor of 2.
Cancel the common factor.
252+100⋅522
Divide 1 by 1.
252+100⋅51
252+100⋅51
Evaluate the exponent.
252+100⋅5
252+100⋅5
Simplify the expression.
Multiply 100 by 5.
252+500
752
752
Rewrite 752 as 42⋅47.
Factor 16 out of 752.
16(47)
Rewrite 16 as 42.
42⋅47
42⋅47
Pull terms out from under the radical.
447
447
The result can be shown in multiple forms.
Exact Form:
447
Decimal Form:
27.42261840…
Find the Distance Between Two Points (3 square root of 7,-3 square root of 5) , (9 square root of 7,7 square root of 5)

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