HOW TO SIMPLIFY A NESTED RADICAL ?
A nested radical has a square root with in a square root.
Ex 1:
What is it equal to ?
Sol:
Say
= √d ± √e
= √d ± √eSquaring on both sides
a ± b√c = d + e ±
Equating
a = d + e ----- (i)
b√c =
Squaring again
b2c = 4de ---- (ii)
Solving (i) and (ii), we have
Ex 2:
= ?
Sol:
In this problem, a = 5, b = 2, c = 6
Applying the formula
∴ = √3 +
√2 also
= √3 +
√2 also
= √3 –
√2.