Find the positive square root of 36x2+60x+25
Solution:
Step 1: Factorize the given polynomial:
Let p(x)=36x2+60x+25
The given polynomial can be rewritten as:
p(x)=(6x)2+2(6x)(5)+(5)2⇒p(x)=(6x+5)2............(1)[∵(a+b)2=a2+2ab+b2]
Step 2: Find the positive square root of p(x):
p(x)=±(6x+5)2Takingsquarerootofequation(1)=±(6x+5)
Final answer: Hence, the positive square root of 36x2+60x+25is(6x+5).