# Solve for r ( square root of 2)/2=24/r

22=24r
Rewrite the equation as 24r=22.
24r=22
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
24⋅2=r⋅2
Solve the equation for r.
Rewrite the equation as r⋅2=24⋅2.
r⋅2=24⋅2
Multiply 24 by 2.
r⋅2=48
Divide each term by 2 and simplify.
Divide each term in r⋅2=48 by 2.
r⋅22=482
Cancel the common factor of 2.
Cancel the common factor.
r⋅22=482
Divide r by 1.
r=482
r=482
Simplify 482.
Multiply 482 by 22.
r=482⋅22
Combine and simplify the denominator.
Multiply 482 and 22.
r=48222
Raise 2 to the power of 1.
r=482212
Raise 2 to the power of 1.
r=4822121
Use the power rule aman=am+n to combine exponents.
r=48221+1
Add 1 and 1.
r=48222
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
r=482(212)2
Apply the power rule and multiply exponents, (am)n=amn.
r=482212⋅2
Combine 12 and 2.
r=482222
Cancel the common factor of 2.
Cancel the common factor.
r=482222
Divide 1 by 1.
r=48221
r=48221
Evaluate the exponent.
r=4822
r=4822
r=4822
Cancel the common factor of 48 and 2.
Factor 2 out of 482.
r=2(242)2
Cancel the common factors.
Factor 2 out of 2.
r=2(242)2(1)
Cancel the common factor.
r=2(242)2⋅1
Rewrite the expression.
r=2421
Divide 242 by 1.
r=242
r=242
r=242
r=242
r=242
r=242
The result can be shown in multiple forms.
Exact Form:
r=242
Decimal Form:
r=33.94112549…
Solve for r ( square root of 2)/2=24/r

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