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What is the least number to be subtracted from 0.000326 to make it a perfect square.
- a)0.000002
- b)0.000004
- c)0.02
- d)0.04
Correct answer is option 'A'. Can you explain this answer?
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What is the least number to be subtracted from 0.000326 to make it a p...
Solution:
To make 0.000326 a perfect square, we need to subtract the least number from it.
Let's assume the least number to be subtracted is x.
Then, the new number will be 0.000326 - x which is a perfect square.
We need to find the value of x.
Let's express 0.000326 - x as a perfect square.
(√0.000326 - √x)² = 0.000326 - x
0.000326 - 2√0.000326x + x = 0.000326 - x
2x = 2√0.000326x
x = √0.000326x
Squaring both sides, we get
x² = 0.000326x
x² - 0.000326x = 0
x(x - 0.000326) = 0
x = 0 or x = 0.000326
Since we need to subtract the least number, x should be as small as possible.
Therefore, the least number to be subtracted from 0.000326 to make it a perfect square is 0.000326 - x = 0.000326 - 0.000326 = 0.000002.
Hence, the correct answer is option A.
To make 0.000326 a perfect square, we need to subtract the least number from it.
Let's assume the least number to be subtracted is x.
Then, the new number will be 0.000326 - x which is a perfect square.
We need to find the value of x.
Let's express 0.000326 - x as a perfect square.
(√0.000326 - √x)² = 0.000326 - x
0.000326 - 2√0.000326x + x = 0.000326 - x
2x = 2√0.000326x
x = √0.000326x
Squaring both sides, we get
x² = 0.000326x
x² - 0.000326x = 0
x(x - 0.000326) = 0
x = 0 or x = 0.000326
Since we need to subtract the least number, x should be as small as possible.
Therefore, the least number to be subtracted from 0.000326 to make it a perfect square is 0.000326 - x = 0.000326 - 0.000326 = 0.000002.
Hence, the correct answer is option A.
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