What is the least number that should be added to 5470 to get a perfect square also find the square root of the number so obtained?

Answer

Verified

Hint:Here the approach we will use in this question to find the least number to make this perfect square is that we will first find the number which is the greatest perfect number near to the question and then we will subtract it to find the least number.

Complete step by step solution:

$ \left( i \right){\text{ 3169}} $ So we will find the closest square number near to $ {\text{3169}} $ is $ 3249 $ , so the difference between two of them will be given as- $ \Rightarrow 3249 - 3169 = 80 $ Therefore, we can say that $ 80 $ should be the least number which when gets added to $ {\text{3169}} $ will make it a perfect square.Hence, $ \sqrt {3249} = 57 $ $ \left( {ii} \right){\text{ 2765}} $ So we will find the closest square number near to $ 2765 $ is $ 2809 $ , so the difference between two of them will be given as- $ \Rightarrow 2809 - 2765 = 44 $ Therefore, we can say that $ 44 $ should be the least number which when gets added to $ 2765 $ will make it a perfect square.Hence, $ \sqrt {2809} = 53 $ $ \left( {iii} \right){\text{ 36,320}} $ So we will find the closest square number near to $ 36,320 $ is $ 36,481 $ , so the difference between two of them will be given as- $ \Rightarrow 36,481 - 36,320 = 161 $ Therefore, we can say that $ 161 $ should be the least number which when gets added to $ 36,320 $ will make it a perfect square.Hence, $ \sqrt {36,481} = 191 $ $ \left( {iv} \right){\text{ 81,180}} $ So we will find the closest square number near to $ 81,180 $ is $ 81,225 $ , so the difference between two of them will be given as- $ \Rightarrow 81,225 - 81,180 = 45 $ Therefore, we can say that $ 45 $ should be the least number which when added to $ 81,180 $ will make it a perfect square.Hence, $ \sqrt {81,225} = 285 $ $ \left( v \right){\text{ 92,700}} $ So we will find the closest square number near to $ 92,700 $ is $ 93,025 $ , so the difference between two of them will be given as- $ \Rightarrow 93,025 - 92,700 = 325 $ Therefore, we can say that $ 325 $ should be the least number which when gets added to $ 92,700 $ will make it a perfect square.

Hence, $ \sqrt {93,025} = 305 $

Note:

This type of question can also be solved by using the long division method and we can know the least number from there. To solve the above method we have to use the heat and trial method to check the perfect square. I would suggest always checking the number which can be easily squared from there, checking the number around and in this way we can easily find out without much more calculations.

Question 10 Exercise 6.4

Answer:

Solution:

(i) 525

Since remainder is 41.

Therefore $22^2<525<>$

Next perfect square number $23^2=529$

Hence, number to be added

= 529 – 525 = 4

$\therefore525+4=529$

Hence, the square root of 529 is 23.

(ii) 1750

Since remainder is 69.

Therefore $41^2<1750<>$

Next perfect square number $42^2=1764$

Hence, number to be added

= 1764 – 1750 = 14

$\therefore1750+14=1764$

Hence, the square root of 1764 is 42

(iii) 252

Since remainder is 27.

Therefore $15^2<252<>$

Next perfect square number $16^2=256$

Hence, number to be added

= 256 – 252 = 4

$\therefore252+4=256$

Hence, the square root of 256 is 16.

(iv) 1825

Since remainder is 61.

Therefore $42^2<1825<>$

Next perfect square number $43^2=1849$

Hence, number to be added = 1849 – 1825 = 24

$\therefore1825+24=1849$

Hence, the square root of 1849 is 43.

(v) 6412

Since remainder is 12.

Therefore $80^2<6412<>$

Next perfect square number $81^2=6561$

Hence, number to be added

= 6561 – 6412 = 149

$\therefore6412+149=6561$

Hence, the square root of 6561 is 81.

Video transcript

"Hello students. Welcome to lead your homework in this video. We are going to solve this question, which says find the least number which must be added to the given numbers to find or to get a perfect square. And once we do that, we need to find the square root. Okay, so over here it is to find the number that needs to be added. Okay. So let's look at the first one and The first step we need to do is the long division get up here. So let's do long division for this particular number that 525 pay attention that the grouping is to be done from a right to left and not necessarily every single time. You'll have the group that has two numbers in a liquid sample find this is the number that absolutely fine. We'd find a perfect square total five. So that's two twos are four you subtracted you get one. We bring down 25 we need to get a new devices. So we'll multiply the quotient by 2 and I get for now. I need to find another number over here that will Give me an answer to multiply that will be 125 less than 125. So 42 into 2 gives me a default under the closest 125 that I get another practical. I'll get the answer as 40 now. We need to find the number that needs to be added to 525 to get a perfect square. If you pay attention here 22 is the remainder that we're getting on your 41. This means the quotient 22 square the square of a quotient when you will always and always be less than the number given to us or the dividend in this kit is 525 right? So that's what the next number of a Pity to and that's 2320 be square. Forgive me for 29 feet that is a number that is greater than 5 25. That means I need to add a certain number to 525 that I get 520 grams a perfect square. What number were you are divided by 85, right? And for that what you do you would subtract so you will subtract 5 25 from 529 and the answer you get is that means the number that is padded to 525 get a perfect square is 4 and the pocket square is 529. The thing about the question says find the square root of the perfect square that you have found out so over here. We already know that the square root of 5 x 9 is Penalties plus write this down square root of 529 is 23. That's one the second one second one says 1750. Okay. So let's do long division for this one make the pears from the right to left. Okay. The closest perfect square is 4 8 16 one to bring down 500. You'll multiply your quotient with to you'll get it. So now in the number and multiply with and I'll get an answer that is either 1 to 2 less than 50. So 81 into one hears me 81. And as up to the school district 150 and the answer would be 69 the remainder in this case P 69. So in this particular case 41 square is definitely less than 1750. Okay, because I haven't been this excited about a perfect square. So it's more than x number 42 42 squared gives me 1764 which is greater than 1750 so I can add a certain number to figure out what the next perfect square begin to find that I will have to do 1764 - 1750 give me 14 that means I need to add 14. 1750 you be the perfect square that is 1764 and like we've seen here the square root of 1764 is equal to 42. Let's move on to the next one. That's five to 50 to 250. Let's go get up from right to left. Okay, the closest of X by 2 is 1 1 0 1 subtract it I'll get one I'll bring down 52 now what I do I will have to multiply my quotient with so 2 into 1 is 2 and I will find another number on multiplication algorithm of less than 150 200 and the 25 into 5. That gives me 125. That even though in this case is 27. So definitely 15 Square will be less than 250 to the next number 15 is 16 which is 256 16 squares. So 56 right? There you go. I just yes 26. So now 256 is greater than 250 go that if I can figure out what number needs to be added to torpedo to give me 250 604 lat I have to subtract 256 the specifics - 252 and get the answer is 4 that means the number that needs to be added to 250. It's flexible 52 plus 4 will give me a perfect square. That's 256 and we know the square root of 256 is. You gonna hang out how to solve this feel free to pause the video went so the other some spiders are gonna come back and cross check how it's done. It'll help you with your practice. Okay. It's the photo 1825 lets you belong to a method on this that group it was from right to left. The closest perfect square is 16. That's two I'll bring down the 25 and multiply the quotient which due to give me a new budget for the new device or and this case 80 2 into 2 gives me 164. The remainder would be 61. This means that 42 Square would definitely be less than 1825. I need a number that needs to be added to any prefer to give me the next office. Also 43 Square. Let's check for that quantity squared is 1849 just be So to find out what number I need to add and subtract money to fight over money for 9 24 9 - 1825 is equal to 20. So the number that I need to add 20 to 5 is 20 x 20 to 5 plus 24 is equal to 184 9 and the square root for 1849. We know is 43 square root of 1849 is equal to 40. That's what the last one. That's the fifth one here. That is 6412. Let's go them up from right to left 6112. So it's a pizza 64 0 and bring down 12. Yeah. Now we are very very important. Don't just leave it here because it's just 12 and if you multiply this into two you say Okay 60 with anyone other than to and what number do we add your letter don't just leave it original complete the deputy editor window in this case. It's definitely that it needs to be 0 right. That's something less than 12. So 160 into 0. We do see one let me subtract it. You'll get the development. This is where you end your long division with remainder. I'm just gues feeling it e square is less than 6412 eating 1 square is equal to 6 5 6 1. Okay and fine what number I need to add to 6 4 1 2 to get 6 561 I have to subtract 5 6 5 6 1 - 6 4 1 2 gives me 149 that me. The number that needs to be added to 6412 is 149 so that you get the next perfect square then you're just perfect for the six five six months and we know that the square root of six five. 6 1 is equal to 84 when it comes up here to this particular video. Feel free to leave a comment you have any additional then? We'll try our best me back to you. Feel free to like share and comment to a new practice. I see you. There we go. Thank you so much"

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