Problem on Algebraic Surds

Surd with an algebraic expression can be simplified as shown in the example below.
Finding cube root and square root are basic of surd.


Topic : Solving a surd

In the problem shown below explains how to find square root of any algebraic expressions and how to verify the solutions. For more problems on surd you can see indice math.

Problem : Solve algebraically and check your potential solutions: √(t +12) − t = 0

(Alternately, you may type √x as square root(x) and show raising
to the nth power as ^n)

Solution :

√(t +12) − t = 0

square root(t + 12) - t = 0

Squaring both the sides we get..

t + 12 = t^2

=> 0 = t^2 – t – 12

=> t^2 – t - 12 = 0

=> t^2 – 4t + 3t – 12 = 0

=> t(t – 4) + 3(t – 4) = 0

=> (t – 4)(t + 3) = 0

=> t – 4 = 0 and t + 3 = 0

=> t = 4 and t = -3

Now verifying the solutions

when t = 4

L.H.S = root(t + 12) – t

= root(4+12) – 4

= root(16) – 4

= 4 – 4

= 0

= R.H.S

Hence t = 4 is a solution of the given equation.

when t = -3

L.H.S = root(t + 12) – t

= root(-3+12) – (-3)

= root(9) + 3

= -3 + 3

= 0

= R.H.S

Hence t = -3 is a solution of the given equation.



Hope the problem did the needful and for more queries related to the topic please write to our algebra help.