Anandhu J 23rd Apr, 2019

Finding square roots come in almost every mathematics syllabus from 8th class. Its simple to find the square root of perfect square that is one which does not give a decimal square root. But there are others that are not perfect squares. These are surds.

Square roots of perfect squares can be found easily by factorization. But such a method cannot be used for finding square root of surds. We can find the root of 4 or 144 with the help of factorization but we need the help of long division method to find square root of surds (for example root of 2, 3, 5 etc.).

The method of doing square root can be learnt by visiting https://www.math-only-math.com/square-root-of-numbers-that-are-not-perfect-squares.html

Preetham 23rd Apr, 2019

Hello.

Let √(19+6√2) = √a + √ b

Squaring both sides

{√(19+6√2)}^2 = (√a + √ b)^2

19 +6√2 = a+b +2√ab

19 +2√(3x3x2) = a+b +2√ab

Equating rational and irrational parts we get a+b = 19 and ab = 18

By intuition a= 18 and b = 1

So, √(19+6√2) = √18 + √ 1 = 3√2 + 1