Question

by what least number should 2156 the given number be multiplied to get a perfect square number find the number whose square is the new number

Answer 1

Answer :

√2156 = 2×2×7×7×11

11 Should be multiplied 2156 to get a perfect Sqare number

=2156× 11

=2316 is a perfect number of sqare

I hope you Understand

Answer 2

Answer:

If 2156 is multiplied by 11 then it will become perfect Square.

The new number is square of 154.

Step-by-step explanation:

Here given number is 2156.

We want to find which is the least number should 2156 the given number be multiplied to get a perfect square number.

First we need to all factors of 2156.

So,

$2156 = 2 \times 2 \times 7 \times 7 \times 11$

So,

$2156 = {2}^{2} \times {7}^{2} \times 11$

It is clear that if there is one more 11 then 2156 becomes perfect square.

Therefore, required least number be 11.

and

$\sqrt{2156 \times 11} \\ = \sqrt{2 \times 2 \times 7 \times 7 \times 11 \times 11} \\ = 2 \times 7 \times 11 \\ = 154$

The new number is square of 154.

List of some square values upto 30,

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

16² = 256

17² = 289

18² = 324

19² = 361

20² = 400

21² = 441

22² = 484

23² = 529

24² = 576

25² = 625

27² = 729

28² = 784

29² = 841

30² = 900