Math, asked by tanuja86, 2 months ago

3. Is 180 a perfect square? If not, then with what least number should it be multiplied, so that it becomes
a perfect square? What would be the square root of this new number?​

Answers

Answered by devuzhome1
0
No, 180 is not a perfect square.
Th least number should be multiplied is 5. The new number will be 900. The square root of 900 is 30.


Hope this is helping
Answered by Steph0303
1

Answer:

Let's perform the prime factorisation of the number 180.

⇒ 180 = 2 × 2 × 3 × 3 × 5

⇒ 180 = 2² × 3² ×5

We see that all the factors of 180 are having even powers. The condition for a number to be perfect square is to have factors having even powers.

Since the factor 5 doesn't have a pair, we multiply an extra 5 to make it 5², which has an even power.

Hence the number to be multiplied is 5. On multiplying we get:

⇒ 180 × 5 = 900

Now we know that 900 can be written in the form of:

⇒ 2² × 3² × 5²

⇒ √(2² × 3² × 5²) = 2 × 3 × 5

√900 = 30

Hence the square root of the new number 900 is 30.

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