7th Grade Math

Lesson 3C Square Roots 61

Estimating Roots

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Recall the square root of a number is one of its two equal factors.

Similarly, a cube root of a number is one of its three equal factors.

Cube Root

Words A cube root of a number is one of its three equal factors.

Examples Numbers Algebra

2 · 2 · 2 = 8, so √^3 8  If x^3 = y, then (^) √^3 y = x.
Find
3
√ 27. Find
3
√ 125.
Since 3 × 3 × 3 = 27, Since 5 × 5 × 5 = 125,
the cube root of 27 is 3. the cube root of 125 is 5.
You can also estimate cube roots by using 1 = 1^3
8 = 2^3
27 = 3^3
64 = 4^3
125 = 5^3
216 = 6^3
343 = 7^3
512 = 8^3
729 = 9^3
1,000 = 10^3
perfect cubes. The first ten perfect cubes
are shown at the right.
Estimate^3 √ 90 to the nearest whole number.
The first perfect cube less than 90 is 64. √^3  64 = 4
The first perfect cube more than 90 is 125. √^3  125 = 5
34567
(^3643903125)
Since 90 is closer to 64 than 125, √^3 90 is closer to 4 than 5.
So, √^3  90 ≈ 4.
Check Use a calculator. 4 90 4.4814047
4.4814047 rounds to 4. ✓
Find each cube root.
43. √^3 216  44. (^) √^3 1,000  45. √^3  729
Estimate each cube root to the nearest whole number.
Check using a calculator.

46. √^3 35  47. √^3 100  48. √^3  75

The number line shows that

√^3 90 is between 4 and 5.

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