Question

which is the smallest number by which 90 should be a multiplied in order to get a perfect square
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Answer 1

question:

which is the smallest number by which 90 should be a multiplied in order to get a perfect square

solution:

10

To find:

which is the smallest number?

Given:

which 90 should be a multiplied in order to get a perfect square.

step by step explanation:

$\sf 90 = 2×3×3×5$

[ note = see the attachment for prime factorisation ]

here:

3 is a pair but 2 and 5 do not occur in pairs.

so:

$\sf 90 × 2 × 5 = 2 × 3 × 3 × 5 × 2 × 5$

$\sf = 2 × 2 × 3 × 3 × 5 × 5$

now , it becomes perfect square ✔

therefore:

we need to multiply 90 by 2 × 5 i.e 10 to make it a perfect square.

Answer 2

$\red{\sf {Answer:}}$

The smallest number would be 10 if we want to make it smallest number & if we want to multiply it with 90 & get a perfect sqaure.

$\red{\sf {Solution:}}$

First , we need to find multiples so ,

$\pink{\sf {see \: the \: prime \: factorizaton \: mehod \: \: in \: the \: attachmnt \: }}$

Hence , we can see that

$\red{\sf {90 = 2 \times 3 \times 3 \times 5}}$

Here , 3 is having pair and we can see that 2 and 5 is not having any pair.

So , we need to multiply 2 and 5 with 90

$\red{\sf { = 90 \times 2 \times 5}}$

Then,

we will write 2×5 at last when we will write our numbers we have.

First we will write the numbers we have ,

$\red{\sf {2 \times 3 \times 3 \times 5}}$

Then the number which is not having pair we will again multiply it with this numbers

which is ,

$\red{\sf {2 \times 3\times3 \times 5 \times 2 \times 5 }}$

Hence , now we are having two pairs of each number.

$\red{\sf { = 2 \times 2 \times 3 \times 3 \times 5 \times 5}}$

Now , as we know we are now having pairs of each number.

So now we can see that it becomes a perfect square.

Hence,we will multiply 90 by 2×5.

That is , 10 to make it a perfect square.

Hence , we need number 10 to make it a perfect sqaure.