Nested Surds
G)
First I solved the equation using the following steps:
√a+√b= √(a+b+√4ab)
- Here you would simplify the radical by breaking the radicand up into a product of known factors, to give the equation below.
√a+ √b= √(a+b+2√ab)
a+b=a+b+4√ab
- Here I’ve raised both sides to the power of two to eliminate the square roots except the latter part of the right hand side of the equation which is 4√ab.
a-a+b-b=4√ab
- Rearranging the equation leaves me with this.
0=4√ab
Therefore either a=0 or b=0 if the equation is to be satisfied. When a=0, b can equal any other positive value including zero. This is because when you substitute the values in for a and b, suppose if b=5 and a=0:
√0+ √5= √(0+5+√4×0×5)
When simplified , the equation is proved true as you will end up with √5=√5 which is without a doubt completely accurate. Similarly, when b=0 , a can equal any other positive value including zero. In conclusion, for this particular equation to be satisfied either a or b has to equal zero and the other value can be equivalent to any positive number.