Lesson 6 of 1524
Exponents and square roots
An exponent counts repeated multiplication. A square root undoes a square.
Practice this chapter2⁵ means 2 × 2 × 2 × 2 × 2, which is 32. The exponent is a count, not the number you multiply by.
A square root asks which nonnegative number, times itself, gives this result. √49 = 7 because 7 × 7 = 49.
In compound interest, (1 + r)^t means you multiply (1 + r) by itself t times. (1.1)² is 1.21, not 2.2.
Distance in a right triangle
c = √(a² + b²)
Square the legs, add, then take one square root.
Worked example
A right triangle has legs 3 and 4. How long is the third side?
- 1The third side is the hypotenuse, the side opposite the right angle: c = √(a² + b²).
- 2Square each leg before you add: 3² = 9 and 4² = 16.
- 3Add under the square root: 9 + 16 = 25. The expression is now √25.
- 4√25 = 5, because 5 × 5 = 25. A length is not negative, so the root you want is 5, not −5.
Result: 5
Why. The squares of the legs add to the square of the hypotenuse: 9 + 16 = 25, and 25 is 5 squared. Taking the roots first, √9 + √16 = 7, is a different and wrong calculation.
√(9 + 16) is not √9 + √16. Add under the root first, then take one square root.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.