By what smallest number must 180 be multiplied so that the product becomes a perfect square. Also, find the square root of the perfect square obtained.
Answers
Answer:
x
Step-by-step explanation:
value of x = y
and value of y = x
Answer:
The least number is 5 and the “square root” is 30.
Solution:
To find the “smallest number” by which 180 will be multiplied to get a “perfect square”, we need to factorize 180 as under:
180=2 \times 90180=2×90
=2 \times 9 \times 10=2×9×10
=2 \times 3 \times 3 \times 2 \times 5=2×3×3×2×5
=2^{2} \times 3^{2} \times 5=2
2
×3
2
×5
Now, 5 is not in square. If 5 is in square, then derived number will be perfect square.
Hence, 180 must be multiplied by 5 to get a “perfect square” as shown below:
180=2^{2} \times 3^{2} \times 5^{2}=4 \times 9 \times 25=900180=2
2
×3
2
×5
2
=4×9×25=900
Now, the square of 900 = 30
Step-by-step explanation:
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