square within a square root gives an absolute value?
√(4x^2 + 12x + 9)
√(2x+3)^2
= 2x+3
Answer says its |2x+3|
Shouldn't the square cancel out the square root such as
√9 = √(3)^2 = 3 obviously its not |3|
anyone help on this?
√(4x^2 + 12x + 9)
√(2x+3)^2
= 2x+3
Answer says its |2x+3|
Shouldn't the square cancel out the square root such as
√9 = √(3)^2 = 3 obviously its not |3|
anyone help on this?
anonymous
Favorite Answer
if x < -3/2 then your answer(( 2x+3) would be negative. but |2x+3| gives positive answer irrespective of whether x < -3/2 or not
kumorifox
No. Because the squaring is done first due to the brackets, you end up with a positive number. The square root can then be either positive or negative.
√9 = |3|, since (-3)² = 9 and 3² = 9.
√(3)² = √9, which is |3| as described above.
Monica
A square root cannot be negative, thus the number or equation must always be positive. You will see negative roots, but for this you have to use imaginary numbers. Also, squaring a number always gives a positive number.
*Absolute value is always positive.