Question

Find the smallest number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 1280. Solving methods

Answer 1

Therefore 180 must be multiplied by 5 to make it a perfect square. Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square.

Answer 2

Step-by-step explanation:

Given :-

1280

To find :-

Find the smallest number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained ?

Solution :-

Given number = 1280

1280 can be written as

1280 = 2×2×2×2×2×2×2×2×5

1280 = (2×2)×(2×2)×(2×2)×(2×2)×5

It is clear that

5 should be multiplied to get the perfect square number.

On multiplying 1280 with 5 then

=> 1280×5

=> 6400

The square number = 6400

6400 can be written as

6400 = 2×2×2×2×2×2×2×2×5×5

=> 6400 = (2×2)×(2×2)×(2×2)×(2×2)×(5×5)

Square root of 6400

=> √6400

=> √[(2×2)×(2×2)×(2×2)×(2×2)×(5×5)]

=> 2×2×2×2×5

=> 80

Therefore, √6400 = 80

Answer :-

The smallest number should be multiplied with 1280 to get a perfect square number = 5

The square root of the obtained number = 80

Used Method :-

• Prime Factorization method

Used formulae :-

• The number obtained by multiplying the number twice itself is called a square number.

• Numbers can be written as the product of two same numbers are called Perfect square numbers.

Ex:- 1=1×1 , 4=2×2 , 100=10×10 ,...