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?
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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
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
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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