Maths Tricks for square Roots – Formulas

Square Roots

Basic formulas in Powers and Roots

Some basic formulas used to solve questions on exponents are:

• (a^m)ⁿ = (aⁿ)^m = a^mn

• a^m.aⁿ = a^m+n

• a^-m = 1/a^m

• a^m/aⁿ = a^m-n = 1/a^n-m

• (ab)ⁿ = aⁿbⁿ

• (a/b)ⁿ = aⁿ/bⁿ

• a = 1

Some basic formulae used to solve questions on roots are:

• ⁿ√a = a^1/n

• ⁿ√ab = ⁿ√a* ⁿ√b

• ⁿ√(a/b) = ⁿ√a / ⁿ√b

• (ⁿ√a)ⁿ = a

Solved Examples

Question 1:

What is the square root of 144?

Solution:

The factors of 144 are given as,
144 = 12×12
$\sqrt{144}=\sqrt{12\times 12}$ $\sqrt{144}=12$

Question 2:

What is the square root of 80?

Solution:

The factors of 80 are given as,

80= 4×4×5

$\sqrt{80}=\sqrt{4\times 4\times 5}$ $\sqrt{80}=4\sqrt{5}$