Question

2×2=4 3×3=10 4×4=18 5×5=28 6×6=​

Answer 1

Answer:

40

Explanation:

There are more than one method to find the answer.

Three methods are given...

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⇒ First method:

Consider only the RHS.

4, 10, 18, 28

Take the differences between each consecutive terms, so that they form an AP,

6, 8, 10...

The next difference is 12. So 12 is added to 28 to get the next term 12 + 28 = 40.

4 + 6 = 10

10 + 8 = 18

18 + 10 = 28

28 + 12 = 40

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⇒ Second method:

2 × 2 = 2 × 2 + 0 = 4 + 0 = 4

3 × 3 = 3 × 3 + 1 = 9 + 1 = 10

4 × 4 = 4 × 4 + 2 = 16 + 2 = 18

5 × 5 = 5 × 5 + 3 = 25 + 3 = 28

∴ 6 × 6 = 6 × 6 + 4 = 36 + 4 = 40

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⇒ Third method:

Use the formula (n + 1)(n + 1) = n(n + 3), so that,

2 × 2 = (1 + 1)(1 + 1) = 1(1 + 3) = 1 × 4 = 4

3 × 3 = (2 + 1)(2 + 1) = 2(2 + 3) = 2 × 5 = 10

4 × 4 = (3 + 1)(3 + 1) = 3(3 + 3) = 3 × 6 = 18

5 × 5 = (4 + 1)(4 + 1) = 4(4 + 3) = 4 × 7 = 28

∴ 6 × 6 = (5 + 1)(5 + 1) = 5(5 + 3) = 5 × 8 = 40

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Thank you...

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

6 × 6 = 40

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

→2×2=4

→3×3=10

→4×4=18

→5×5=28

To find :

6 × 6 = $\boxed{?}$

Solution :

The numbers are multipled and then added by 0, then 1, then 2 and so on.....

★ 2 × 2 = 4

$\tt{\implies}$ 2 × 2 + 0

$\tt{\implies}$ 4 + 0

$\tt{\implies}$ 4

★ 3 × 3 = 10

$\tt{\implies}$ 3 × 3 + 1

$\tt{\implies}$ 9 + 1

$\tt{\implies}$ 10

★ 4 × 4 = 18

$\tt{\implies}$ 4 × 4 + 2

$\tt{\implies}$ 16 + 2

$\tt{\implies}$ 18

★ 5 × 5 = 28

$\tt{\implies}$ 5 × 5 + 3

$\tt{\implies}$ 25 + 3

$\tt{\implies}$ 28

Following the above logic

★ 6 × 6 =

$\tt{\implies}$ 6 × 6 + 4

$\tt{\implies}$ 36 + 4

$\tt{\implies}$ 40

$\therefore$ 6 × 6 = 40

$\therefore$ 6 × 6 gives the answer 40