Properties of the arithmetic square root
Find roots of squares, products, quotients and powers with the properties of the arithmetic square root, as in the Grade 8 Ukrainian book. Section: Grade 8, arithmetic square root; nth roots are in the Grade 10 studio.
- Germany: grade 9
- Ukraine: grade 8
- Russia: grade 8
Guide
In the Ukrainian programme the properties of the arithmetic square root are Grade 8 algebra, §2 item 15.
For every number a: √(a2) = |a|. For a ≥ 0 and b ≥ 0: √(ab) = √a·√b. For a ≥ 0 and b > 0: √(ab) = √a√b.
The root of a power with an even index: √(a2n) = |an|. These help with roots of decimals and mixed numbers by splitting the number into factors.
Type the answer in the box: a fraction, a decimal or a whole number.