Method 1

All numbers are positive. So answer is not negative.

There is addition, so answer > 0

Simply calculate some values to see if answer is 1 or 3.

We have more terms so that means (0.4 + 0.3 + 0.3 + …)

goes above 1. So answer is 3.

Method 2

We have square root sign in the denominator. To remove it, rationalize the fractions.

Use the opposite sign while rationalizing. On rationalizing we get

Here, A × B does not mean multiplication.

It only signifies the expression A² + B²

So,

6 × (2 × 4)

6 × (2² + 4²

6 × (4 + 16)

6 × 20

6² + 20²

36 + 400

436

While simplifying always followrules of VBODMAS

Order of simplification will be

V – Brackets – Go from inner bracket to outer bracket

6 × (2 × 4)

O – of operation

D - Division

M – Multiplication

A - Addition

S – Subtraction

Here, first we will solve brackets

Let, a = 0.72 and b = 0.39

So the expression can be written as

Standard Formula

a³ - b³ = (a – b)(a² + ab + b²)

The expression can be written as

a – b = 0.72 – 0.39 = 0.33

2² + 6² + 9² ….. + 30² can be written as (3 × 1)² + (3 × 2) ² + (3 × 3)² + ….. + (3 × 10)²

That gives us 3² × 1² + 3² × 3² + …… + 3² × 10²

3² (1² + 2² + 3² + ….. + 10²) = 9 × 385 = 3465