Find the least number to be subtracted from 14165 so as to get a perfect square. Also find the square root of the perfect square so obtained.
Share
Find the least number to be subtracted from 14165 so as to get a perfect square. Also find the square root of the perfect square so obtained.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
4 is the correct answer
Step-by-step explanation:
see the attachment
plz mark me as a brilliant for my next rank
[tex]\large\underline{\sf{Solution-}}[/tex]
Given number is 14165.
So, we have to find the smallest number that must be subtracted from 14165 to make it perfect square.
So, using Long Division Method, we have
[tex]\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:119 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:14165 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: 1 \: \: \: \: \: \:\:}} \\ {\underline{\sf{21}}}& {\sf{\:\: \: \: \: 41 \: \: \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 21\: \: \: \: \:\:}} \\ {\underline{\sf{229}}}& {\sf{\: \: \:2065 \:\:}} \\{\sf{}}& \underline{\sf{\:\:2061\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: 4\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}[/tex]
So, it implies 4 must be subtracted from 14165 to make it a perfect square.
So, Required number = 14165 - 4 = 14161
Now,
[tex]\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:119 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:14161 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: 1 \: \: \: \: \: \:\:}} \\ {\underline{\sf{21}}}& {\sf{\:\: \: \: \: 41 \: \: \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 21\: \: \: \: \:\:}} \\ {\underline{\sf{229}}}& {\sf{\: \: \:2061 \:\:}} \\{\sf{}}& \underline{\sf{\:\:2061\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: 0\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}[/tex]
Hence,
[tex]\rm \implies\:\boxed{ \tt{ \: \sqrt{14161} = 119 \: }}[/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬