Question

by what least number should 2925 be multiplied to get a perfect square find the number whose square is new numberहे गाइस प्लेस प्लीज आंसर मी फास्ट ​

Answer 1

Given :

Number 2925  

To find :

•  Least number that should be multiplied to 2925 to get a perfect square
• Square root of new Number  

Procedure :

• First of all find , prime factor of given number
• Find prime factor, which are in pair , and which are not  Multiply the given number by prime factor which is not in pair.
• The number we get ,will be perfect square
• Now find square root of new Number    

Solution :  

Part 1 -  Prime factor of 2925

$\Large{ \begin{array}{c|c} \tt 3 & \sf{2925} \\ \cline{1-2} \tt 3 & \sf {975 } \\ \cline{1-2} \tt 5 & \sf{ 325} \\ \cline{1-2} \tt 5 & \sf{ 65} \\ \cline{1-2} \tt 13 & \sf{13}\\ \cline{1-2} \tt  & \sf{ 1 } \end{array}}$  

{ Note - User using app , see attachment for same }

➝ 2925 = 3×3×5×5×13  

➝ 2925 = (3×3)×(5×5)×13

So , we have to multiply 2925 by 13 so to get perfect square,  

➝ New Number = 2925 × 13  

➝ New Number = 38025

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Part 2 - Square root of new number  

➝ 38025 = 2925×13  

➝ 38025 = (3×3)×(5×5)×13 × 13  

➝ 38025 = (3×3)×(5×5)×(13×13)  

➝ 38025 = 3² × 5² × 13²  

➝ 38025 = (3×5×13)²  

➝ √38025 = √ (3×5×13)²  

➝ √38025 = 3×5×13 = 195  

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ANSWER :

1) 2925 should be multiplied by 13 to get perfect square

2) Square root of new Number = 195