Simplify Radical Expressions
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Thealgebraicexpressionsinsidethesquarerootsymbolarereferredasradicalexpression
whereasthesquarerootsymbolisreferredasradical.Theexpressionswithradicalsymbolare
definedasthenumbertimeitselftothestatedexpression.Theradicalsymbolpresentinthe
expressionscanbeeasilysolvedbytheperformofsquaringoperationsforthegivenradical
expressions.Theexampleradicalexpressionproblemsaregivenbelowforsolving.
SolvingRadicalExpressions
Belowareexamplesshowinghowtosolveradicalexpressionsbysimplification:
Example1:Solvemyradicalexpression.
[sqrt(3y5)=y1]
Solution:Givenequationis
[sqrt(3y5)=y1]
Forsolvingtheradicalsymbolperformsquaringoperationonbothsides
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Forsolvingtheradicalsymbolperformsquaringoperationonbothsides
[[sqrt(3y5)]^2=(y1)^2]
Simplifytheaboveequation3y5=y22y+1
Changetheaboveequationinfactorform.y25y+6=0
Theaboveequationisinquadraticequationformresultstwosolutions
y=2andy=3istheanswer.
Example2:Solvemyradicalexpression.[sqrt(y^211y+37)=3]
Solution:Givenequationis
[sqrt(y^211y+37)=3]
Forsolvingtheradicalsymbolperformsquaringoperationonbothsides
[[sqrt(y^211y+37)]^2=(3)^2]
Andsimplify.
y211y+37=9
ReadMoreDividingRationalExpressions
Maketheaboveequationinfactorform.y211y+28=0
Theaboveequationisinquadraticequationformresultstwosolutions
y=7andy=4istheanswer.
Example3:Solvemyradicalexpression.
[sqrt(y^210y+25)=1]
Solution:Givenequationis[sqrt(y^210y+25)=1]
Forsolvingtheradicalsymbolperformsquaringoperationonbothsides
[[sqrt(y^210y+25)]^2=(1)^2]
Andsimplify.
y210y+25=1
Maketheaboveequationinfactorform.
y210y+24=0
Theaboveequationisinquadraticequationfo
rmresultstwosolutions
y=6andy=4istheanswer.
PracticeProblems
(1)Solvemyradicalexpression.
[sqrt(4y11)=y2]
Answer:y=3andy=5
2)Solvemyradicalexpression.
[sqrt(y^29y+29)=3]
Answer:y=4andy=5.
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