Question

fimd the smallest natural number by which 968 and 14175 should be divided to make the quotient perfect square. find the square root of the resulting number pls answer step by step ​

Answer 1

Step-by-step explanation:

Given :-

968 and 14175

To find :-

Find the smallest natural number by which 968 and 14175 should be divided to make the quotient perfect square. find the square root of the resulting number ?

Solution :-

Given numbers are 968 and 14175

986 can be written as

968 =( 2×2)×2×(11×11)

If 968 is divided by 2 then it becomes a perfect square.

968/2 = 484

The resulting number = 484

Square root of 484

=√484

= √[(2×2)×(11×11)]

= 2×11

= 22

and

14175 can be written as

14175 = (3×3)×(3×3)×(5×5)×7

If we divide 14175 by 7 then it becomes a perfect square number.

=> 14175/7

=> 2025

The resulting number = 2025

Square root of 2025

=√2025

=√[(3×3)×(3×3)×(5×5)]

= 3×3×5

=45

Answer :-

(1) 968 should be divided by 2 so that it becomes a perfect square number.

The square root of the resulting number is 22

(2)14175 should be divided by 7 so that it becomes a perfect square number.

The square root of the resulting number is 45

Used Method:-

• Prime factorization method

Perfect square number:-

• The number which can be written as the product of same number is called a perfect square number.

Ex:-1=1×1

4=2×2....