Which number should be multiplied to 1575 to make it a square number 4 5 6 7

(i) 1575

At first,

We’ll resolve the given number into prime factors:

Hence,

1575 = 7 × 25 × 9

= 7 × 3 × 3 × 5 × 5

= (5 × 3) × (5 × 3) × 7

In the above factors only 7 is unpaired

So, in order to get a perfect square the given number should be divided by 7

Hence,

The number whose perfect square is the new number is as following:

= (5 × 3) × (5 × 3)

= (5 × 3) × (5 × 3)

= (5 × 3)2

= (15)2

(ii) 9075

At first,

We’ll resolve the given number into prime factors:

Hence,

9075 = 121 × 25 × 3

= 11 × 11 × 3 × 5 × 5

= (5 × 11) × (5 × 11) × 3

In the above factors only 3 is unpaired

So, in order to get a perfect square the given number should be divided by 3

Hence,

The number whose perfect square is the new number is as following:

=(5 × 11) × (5 × 11)

= (5 × 11)2

= (55)2

(iii) 4851

At first,

We’ll resolve the given number into prime factors:

Hence,

4851 = 11 × 49 × 9

= 11 × 3 × 3 × 7 × 7

= (7 × 3) × (7 × 3) × 11

In the above factors only 11 is unpaired

So, in order to get a perfect square the given number should be divided by 11

Hence,

The number whose perfect square is the new number is as following:

=(7 × 3) × (7 × 3)

= (7 × 3)2

= (21)2

(iv) 3380

At first,

We’ll resolve the given number into prime factors:

Hence,

3380 = 4 × 5 × 169

= 2 × 13 × 13 × 2 × 5

= (2 × 13) × (2 × 13) × 5

In the above factors only 5 is unpaired

So, in order to get a perfect square the given number should be divided by 5

Hence,

The number whose perfect square is the new number is as following:

=(2 × 13) × (2 × 13)

= (2 × 13)2

= (26)2

(v) 4500

At first,

We’ll resolve the given number into prime factors:

Hence,

4500 = 4 × 125 × 9

= 2 × 2 × 3 × 3 × 5 × 5 × 5

= (5 × 3 × 2) × (5 × 3 × 2) × 5

In the above factors only 5 is unpaired

So, in order to get a perfect square the given number should be divided by 5

Hence,

The number whose perfect square is the new number is as following:

=(5 × 3 × 2) × (5 × 3 × 2)

= (5 × 2 × 3) × (5 × 2 × 3)

= (5 × 2 × 3)2

= (30)2

(vi) 7776

At first,

We’ll resolve the given number into prime factors:

Hence,

7776 = 32 × 243

= 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 2

= (2 × 2 × 3 × 3) × (2 × 2 × 3 × 3) × 2 × 3

In the above factors only 2 and 3 are unpaired

So, in order to get a perfect square the given number should be divided by 6

Hence,

The number whose perfect square is the new number is as following:

= (2 × 2 × 3 × 3) × (2 × 2 × 3 × 3)

= (2 × 2 × 3 × 3)2

= (36)2

(vii) 8820

At first,

We’ll resolve the given number into prime factors:

Hence,

8820 = 4 × 5 × 9 × 49

= 2 × 2 × 3 × 3 × 7 × 7 × 5

= (7 × 3 × 2) × (7 × 3 × 2) × 5

In the above factors only 5 is unpaired

So, in order to get a perfect square the given number should be divided by 5

Hence,

The number whose perfect square is the new number is as following:

=(7 × 3 × 2) × (7 × 3 × 2)

= (7 × 3 × 2)2

= (42)2

(viii) 4056

At first,

We’ll resolve the given number into prime factors:

Hence,

4056 = 8 × 3 × 169

= 2 × 2 × 13 × 13 × 3 × 2

= (13 × 2) × (13 × 2) × 6

In the above factors only 6 is unpaired

So, in order to get a perfect square, the given number should be divided by 6

Hence,

The number whose perfect square is the new number is as following:

=(13 × 2) × (13 × 2)

= (13 × 2)2

= (26)2

 1575 = 3 x 3 x 5 x 5 x 7 

Grouping them into pairs of equal factors:
1575 = (3 x 3) x (5 x 5) x 7
The factor, 7 is not paired. For a number to be a perfect square, each prime factor has to be paired. Hence, 1575 must be divided by 7 for it to be a perfect square.
The new number would be (3 x 3) x (5 x 5).
Furthermore, we have:
(3 x 3) x (5 x 5) = (3 x 5) x (3 x 5)
Hence, the number whose square is the new number is:
3 x 5 = 15

Here, prime factor 7 has no pair. Therefore 252 must be multiplied by 7 to make it a perfect square.

\therefore252\times7=1764

And (i) \sqrt{1764}=2\times3\times7=42

(ii) 180 = 2 x 2 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.

\therefore180\times5=900

And \sqrt{900}=2\times3\times5=30

(iii) 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square.

\therefore1008\times7=7056

And \sqrt{7056}=2\times2\times3\times7=84

(iv) 2028 = 2 x 2 x 3 x 13 x 13

Here, prime factor 3 has no pair. Therefore 2028 must be multiplied by 3 to make it a perfect square.

\therefore2028\times3=6084

And \sqrt{6084}=2\times2\times3\times3\times13\times13=78

(v) 1458 = 2 x 3 x 3 x 3 x 3 x 3 x 3

Here, prime factor 2 has no pair. Therefore 1458 must be multiplied by 2 to make it a perfect square.

Is 1575 is a perfect square?

What is the smallest number by which 1575 can be multiplied so that the product is a perfect square?

What number should 1575 be divided to get a perfect square also find the number whose square is the new number?

Which number must be multiplied by (