Practice Square roots
The square root of a nonnegative number is the nonnegative number whose square equals it.
Square roots connect square areas to side lengths.
Exercises with solutions
Taking a root reverses squaring: √25 = 5 because 5² = 25. The root of a number is the non-negative number whose square gives that number. You may not take roots of sums term by term.
Exercise 1
Calculate √81.
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9
9 · 9 = 81, so √81 = 9.
Exercise 2
Calculate √144.
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12
12 · 12 = 144, so √144 = 12.
Exercise 3
Calculate √(9 + 16).
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5
Add first: 9 + 16 = 25. Then √25 = 5. Wrong would be √9 + √16 = 3 + 4 = 7.
Exercise 4
Between which whole numbers does √50 lie?
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between 7 and 8
7² = 49 and 8² = 64. Since 50 lies between 49 and 64, √50 lies between 7 and 8.
Common mistake
Taking the root of a sum term by term: √(9 + 16) is 5, not 7. And confusing the root with the solution: for x² = 25 both x = 5 and x = −5 are solutions, but √25 is only the positive number 5.
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