Math, asked by vangoghbetty934, 4 months ago

show that the difference between the 7th square number and the 4th square number is multiple of 3

Answers

Answered by xTvTx

Answer:

Step-by-step explanation:

First multiple by 3 and substructure 21 and 12

Answered by vinod04jangid

Answer: 7th square number - 4th square number $=$ $7^{2}$ - $4^{2}$

$=$ $49 - 16$

$= 33$

and factor of 33 is 1 × 3 × 11.So 33 is multiple of 11 of 3.

∴The difference between the 7th square number and the 4th square number is multiple of 3.

Step-by-step explanation:

Given:7th square number = $7^{2}$ = 49

4th square number = $4^{2}$ = 16

To find:We have to find the difference between the 7th square number and the 4th square number which is multiple of 3.

Explanation:

Step 1:The 7th square number = $7^{2}$ = 49

Step 2:The 4th square number = $4^{2}$ = 16

Step 3:Now the difference between 7th square number and 4th square number is given by,

⇒ 7th square number - 4th square number $=$ $7^{2}$ - $4^{2}$

$=$ $49 - 16$

$= 33$

Step 4: On finding the factor of 33 we get,

$33 =$ $1$ × $3$ × $11$

Step 5:From the factor of 33 we can see that 33 is multiple of 11 of 3

∴ The difference between the 7th square number and the 4th square number is multiple of 3.

Concept:

1st square number = 1 × 1 = 1

2nd square number = 2× 2 = 4

3rd square number = 3 × 3= 9

4th square number = 4× 4 = 16

5th square number = 5 × 5 = 25

6th square number = 6 × 6 = 36

7th square number = 7 × 7 = 42

8th square number = 8 × 8 = 64

9th square number = 9 × 9 = 81 etc.

#SPJ2

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