Question

By what least number should the given number be multipled to get a perfect square number? in each case, find the number whose square is new jumber.

• 2156
• 3380
• 2475
• 9075
​

Answer 1

Answer:

3380

Prime factorisation : 2 × 2 × 5 × 13 × 13

.°. We'll multiply 5 to get a perfect square.

Number obtained after multiplying =  

Square root =  

_____❤

7623

Prime factorisation : 3 × 3 × 7 × 11 × 11

.°. We'll multiply 7 to get a perfect square.

Number obtained after multiplying =  

Square root =  

_____❤

3332

Prime factorisation : 2 × 2 × 7 × 7 × 17

.°. We'll multiply 17 to get a perfect square.

Number obtained after multiplying =  

Square root =  

_____❤

Step-by-step explanation:

Answer 2

$\underline{ \underline{ \Large \pmb{\sf { {Required \: Answer :}} }} }$

Here, it's given that by which least number should the given number (2156, 3380, 2475 & 9075) be multiplied to get a perfect square number. And we have to find the number whose perfect square is new number.

• Firstly, we'll find the prime factors of the given number by using prime factorization method. And, after resolving the prime factors, we'll get a factor which doesn't contains any square. Thus, we have to multiply it with the given number & finally we'll get our required answer.

${ \underline{ \underline{ \sf{ \blue{Calculating \: for \: 2156 : }}}}}$

Prime factorization of 2156,

$\begin{array}{c | c} \sf{ \sf \underline{2}}& \sf\underline{2156} \\\sf{ \underline{2}} & \sf \underline{1078} \\\sf{ \underline{7}}& \sf \underline{539} \\\sf{ \underline{7}} & \sf \underline{77} \sf \\\sf{ \underline{11}}& \sf \underline{11} \\ & \sf1\end{array}$

By prime factorization, we got the prime factors as,

→ 2156 = 2 × 2 × 7 × 7 × 11

→ 2156 = 2² × 7² × 11

For getting a perfect square, we'll multiply 2156 by 11.

$\dashrightarrow$ 2156 × 11

$\rm\dashrightarrow{\pink{\underbrace{\boxed{\blue{\rm{New \: number = 23716}}}}}}$

Therefore, the number whose square is the new number is 23716.

____________________________

${ \underline{ \underline{ \sf{ \blue{Calculating \: for \: 3380 : }}}}}$

Prime factorization of 3380,

$\begin{array}{c | c} \sf{ \sf \underline{2}}& \sf\underline{3380} \\\sf{ \underline{2}} & \sf \underline{1690} \\\sf{ \underline{5}}& \sf \underline{845} \\\sf{ \underline{13}} & \sf \underline{169} \sf \\\sf{ \underline{13}}& \sf \underline{13} \\ & \sf1\end{array}$

By prime factorization, we got the prime factors as,

→ 3380 = 2 × 2 × 5 × 13 × 13

→ 3380 = 2² × 5 × 13²

For getting a perfect square, we'll multiply 3380 by 5.

$\dashrightarrow$ 3380 × 5

$\rm\dashrightarrow{\pink{\underbrace{\boxed{\blue{\rm{New \: number = 16900}}}}}}$

Therefore, the number whose square is new number is 16900.

_____________________________

${ \underline{ \underline{ \sf{ \blue{Calculating \: for \: 2475 : }}}}}$

Prime factorization of 2475,

$\begin{array}{c | c} \sf{ \sf \underline{3}}& \sf\underline{2475} \\\sf{ \underline{3}} & \sf \underline{825} \\\sf{ \underline{5}}& \sf \underline{275} \\\sf{ \underline{5}} & \sf \underline{55} \sf \\\sf{ \underline{11}}& \sf \underline{11} \\ & \sf1\end{array}$

By prime factorization, we got the prime factors as,

→ 2475 = 3 × 3 × 5 × 5 × 11

→ 2475 = 3² × 5² × 11

For getting a perfect square, we'll multiply 2475 by 11.

$\dashrightarrow$ 2475 × 11

$\rm\dashrightarrow{\pink{\underbrace{\boxed{\blue{\rm{New \: number = 27225}}}}}}$

Therefore, the number whose square is the new number is 27225.

______________________________

${ \underline{ \underline{ \sf{ \blue{Calculating \: for \: 9075 : }}}}}$

Prime factorization of 9075,

$\begin{array}{c | c} \sf{ \sf \underline{3}}& \sf\underline{9075} \\\sf{ \underline{5}} & \sf \underline{3025} \\\sf{ \underline{5}}& \sf \underline{605} \\\sf{ \underline{11}} & \sf \underline{121} \sf \\\sf{ \underline{11}}& \sf \underline{11} \\ & \sf1\end{array}$

By prime factorization, we got the prime factors as,

→ 9075 = 3 × 5 × 5 × 11 × 11

→ 9075 = 3 × 5² × 11²

For getting a perfect square, we'll multiply 9075 by 3.

$\dashrightarrow$ 9075 × 3

$\rm\dashrightarrow{\pink{\underbrace{\boxed{\blue{\rm{New \: number = 27225}}}}}}$

Therefore, the number whose square is the new number is 27225.