# Simplify ( square root of 3 6/7- square root of 1 5/7)÷( square root of 3/175)

(367-157)÷3175
Convert 367 to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
3+67-1573175
Add 3 and 67.
To write 3 as a fraction with a common denominator, multiply by 77.
3⋅77+67-1573175
Combine 3 and 77.
3⋅77+67-1573175
Combine the numerators over the common denominator.
3⋅7+67-1573175
Simplify the numerator.
Multiply 3 by 7.
21+67-1573175
Add 21 and 6.
277-1573175
277-1573175
277-1573175
277-1573175
Convert 157 to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
277-1+573175
Add 1 and 57.
Write 1 as a fraction with a common denominator.
277-77+573175
Combine the numerators over the common denominator.
277-7+573175
Add 7 and 5.
277-1273175
277-1273175
277-1273175
Simplify the numerator.
Rewrite 277 as 277.
277-1273175
Simplify the numerator.
Rewrite 27 as 32⋅3.
Factor 9 out of 27.
9(3)7-1273175
Rewrite 9 as 32.
32⋅37-1273175
32⋅37-1273175
Pull terms out from under the radical.
337-1273175
337-1273175
Multiply 337 by 77.
337⋅77-1273175
Combine and simplify the denominator.
Multiply 337 and 77.
33777-1273175
Raise 7 to the power of 1.
337717-1273175
Raise 7 to the power of 1.
3377171-1273175
Use the power rule aman=am+n to combine exponents.
33771+1-1273175
Add 1 and 1.
33772-1273175
Rewrite 72 as 7.
Use axn=axn to rewrite 7 as 712.
337(712)2-1273175
Apply the power rule and multiply exponents, (am)n=amn.
337712⋅2-1273175
Combine 12 and 2.
337722-1273175
Cancel the common factor of 2.
Cancel the common factor.
337722-1273175
Divide 1 by 1.
33771-1273175
33771-1273175
Evaluate the exponent.
3377-1273175
3377-1273175
3377-1273175
Simplify the numerator.
Combine using the product rule for radicals.
37⋅37-1273175
Multiply 7 by 3.
3217-1273175
3217-1273175
Rewrite 127 as 127.
3217-1273175
Simplify the numerator.
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
3217-4(3)73175
Rewrite 4 as 22.
3217-22⋅373175
3217-22⋅373175
Pull terms out from under the radical.
3217-2373175
3217-2373175
Multiply 237 by 77.
3217-(237⋅77)3175
Combine and simplify the denominator.
Multiply 237 and 77.
3217-237773175
Raise 7 to the power of 1.
3217-2377173175
Raise 7 to the power of 1.
3217-23771713175
Use the power rule aman=am+n to combine exponents.
3217-23771+13175
Add 1 and 1.
3217-237723175
Rewrite 72 as 7.
Use axn=axn to rewrite 7 as 712.
3217-237(712)23175
Apply the power rule and multiply exponents, (am)n=amn.
3217-237712⋅23175
Combine 12 and 2.
3217-2377223175
Cancel the common factor of 2.
Cancel the common factor.
3217-2377223175
Divide 1 by 1.
3217-237713175
3217-237713175
Evaluate the exponent.
3217-23773175
3217-23773175
3217-23773175
Simplify the numerator.
Combine using the product rule for radicals.
3217-27⋅373175
Multiply 7 by 3.
3217-22173175
3217-22173175
Combine the numerators over the common denominator.
321-22173175
Subtract 221 from 321.
2173175
2173175
Simplify the denominator.
Rewrite 3175 as 3175.
2173175
Simplify the denominator.
Rewrite 175 as 52⋅7.
Factor 25 out of 175.
217325(7)
Rewrite 25 as 52.
217352⋅7
217352⋅7
Pull terms out from under the radical.
217357
217357
Multiply 357 by 77.
217357⋅77
Combine and simplify the denominator.
Multiply 357 and 77.
21737577
Move 7.
217375(77)
Raise 7 to the power of 1.
217375(717)
Raise 7 to the power of 1.
217375(7171)
Use the power rule aman=am+n to combine exponents.
21737571+1
Add 1 and 1.
21737572
Rewrite 72 as 7.
Use axn=axn to rewrite 7 as 712.
217375(712)2
Apply the power rule and multiply exponents, (am)n=amn.
217375⋅712⋅2
Combine 12 and 2.
217375⋅722
Cancel the common factor of 2.
Cancel the common factor.
217375⋅722
Divide 1 by 1.
217375⋅71
217375⋅71
Evaluate the exponent.
217375⋅7
217375⋅7
217375⋅7
Simplify the numerator.
Combine using the product rule for radicals.
2173⋅75⋅7
Multiply 3 by 7.
217215⋅7
217215⋅7
Multiply 5 by 7.
2172135
2172135
Multiply the numerator by the reciprocal of the denominator.
217⋅3521
Cancel the common factor of 21.
Cancel the common factor.
217⋅3521
Rewrite the expression.
17⋅35
17⋅35
Cancel the common factor of 7.
Factor 7 out of 35.
17⋅(7(5))
Cancel the common factor.
17⋅(7⋅5)
Rewrite the expression.
5
5
Simplify ( square root of 3 6/7- square root of 1 5/7)÷( square root of 3/175)

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