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NCERT Solutions Class 8 Mathematics Solutions for Exercise 6.4 in Chapter 6 - Squares and Square Roots
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Q8) A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remains the same. Find the minimum number of plants he needs more for this.
Answer:
Solution:
Here, plants = 1000
Since the remainder is 39.
Therefore 31^2<1000
Next perfect square number 32^2=1024
Hence, number to be added
= 1024 – 1000 = 24
\therefore1000+24=1024
Hence, the gardener required 24 more plants.
Video transcript
Hello kids, welcome to Lido homework in
this video
we are going to answer this question that
states a
the gardener has a thousand plants
he wants to plant these in such a way.
that he has
An equal number of rows and an equal number of
columns
okay find the minimum number of plants
he needs more for this
so instead of trying to imagine a thousand
plants, let's imagine if you have
four plants can you arrange them
in an equal number of rows and equal
number of columns
if you have four plants
can you do something like this great okay
what if I tell you that I'll give you
five plants
can you arrange them in an equal number of
rows and an equal number of columns
no right if there are five then you will
have to add in some more plans to make
An equal number of rows and an equal number of
columns
right but if it was only 4 then you can
See you over here
2 rows and 2 columns also pay attention
4 is a perfect square so you can
conclude that for an equal number of rows
and an equal number of columns the number
of plants
whatever the number of plants it should
be a perfect square
when I told you I'd give you one more
plant
That's nothing but five plants and five
is not a perfect square right so you
will have to add in more plants
to figure out how you will make
the perfect same number of rows and the same
number of columns
okay so in this case what would you do
obviously you have
five you will add in four more
right and then you will make it into
three rows and three
the column that is again nine so the idea
here
is to have an equal number of rows and
The equal number of columns the number of
plants should be perfect
square so let's first check if a thousand
is a perfect square
if you read the question carefully
the question itself says to find the
minimum
number of plants he needs
more for this right that means
Definitely a thousand is not perfect
square but we need to figure out
uh how many more plants will he need
right so let's get into that and for
what will you do, you will take the
number
thousands and then we'll first
find out using the long division method
what could be the possible number of
plants he needs to add
so let's take thousands here and we'll do
the
long division method so for long
division method first
pair up all the numbers in groups of
twos from your right to left
so one pair and another paris
the second step is
to find the perfect square closer to 10
so these three are nine
I'll get one and I'll bring down the
next pair that's a hundred
the next step is to multiply your
quotient with
two you will get it as six
now we need to figure out another number
over here when you will multiply
it you will get a number that is less
Then 100
so that is 61 into 1
The rights will give us 60 1 and the
The rest here is 39
so now since there is a remainder
that means that this is not perfect.
square
we need to find out how many more um
plants that he will need now since this is 39
as a rest
we can see that 31 square
will for sure be less than the number
given to us that's a thousand
Okay, let's move on to the next number
after 31
and that's 32 square
32 square is 1024
okay so I can say that 1000
actually lies between 31 square
and 32 square so
the number of plants additional
that the gardener needs should be a
Perfect Square like we said and the next
The immediate perfect square after 31 is 32
which is 1024
and it's more than a thousand right so
how many more plants will he need
let's take 1024 minus
thousand which is equal to 24
right so a thousand plants that he has
he will add in 24 more
plants right
He will have 1024 plants and now with
this 1024
plants, how many rows and how many
columns he can make since the perfect
square
right its 32 square is 1024
so that means that he can make a number of
rows and number of columns equal if he
add 24 more plants to
1000 okay
hope your doubt for this particular
question uh
is resolved please feel free to like share
and comment and I'll see you in another
video
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