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How To Solve: Roots
Attached pdf of this Article as SPOILER at the top! Happy learning! Hi All,
I have recently uploaded a video on YouTube to discuss
Roots in Detail:
Following is covered in the video
¤ Square root of a number is ALWAYS positive
¤ Simplifying √a * √b
¤ Simplifying \(\frac{√a}{√b}\)
¤ Simplifying \((√a)^n \)
¤ Simplifying √(x ± y)
¤ Simplifying \(a^{(x/y)}\)
¤ Simplifying \(√(a^2)\)
¤ Simplifying √n
Square root of a number is ALWAYS positiveEven root of any number will always be a positive value
Ex: √36 = + 6
Although, \(x^2\) = 36 => x = ± √36 = ±6
Simplifying √a * √b√a * √b = √(ab)
Ex: √2 * √3 = √(2*3) = √6
Simplifying \(\frac{√a}{√b}\)\(\frac{√a}{√b}\) = \(√(\frac{a}{b})\)
Ex: \(\frac{√4}{√2}\) = \(√(\frac{4}{2})\) = √2
Simplifying \((√a)^n \)\((√a)^n\) = √(\(a^n\))
Ex: \((√2)^4\) = √(\(2^4\)) = \(2^2\) = 4
Simplifying √(x ± y)√(x ± y) ≠ √x ± √y
Ex: √(2 + 3) ≠ √2 + √3
=> √5 ≠ √2 + √3
=> 2.23 ≠ 1.414 + 1.732
=> 2.23 ≠ 3.146
Simplifying \(a^{(x/y)}\)\(a^{(x/y)}\) = \(\sqrt[y]{a^x}\)
Ex: \(2^{(6/3)}\) = \(\sqrt[3]{2^6}\) = \(2^2\) = 4
Simplifying \(√(a^2)\)√(\(a^2\)) = |a|
√(\(a^2\)) = -a, when a ≤ 0
√(\(a^2\)) = a, when a ≥ 0
Ex: √(\(3^2\)) = +3 = |3|
√(\((-3)^2\)) = 3 = -(-3) = |-3|
Simplifying √nTo simplify √n, we need to express n in powers of prime numbers and then need to take out the even powers.
Example: √56 = √(4*14) = √((2^2) * 14) = 2√14
Hope it helps!
Good Luck!
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