1-9 Estimate Roots
Estimate to the nearest integer.
1. SOLUTION: The largest perfect square less than 23 is 16. The smallest perfect square greater than 23 is 25. Find the square root
of each number:
So,
and . Write an inequality. Simplify.
is between 4 and 5. Since 23 is closer to 25 than 16, the best whole number estimate for is 5.
2. SOLUTION: The largest perfect square less than 197 is 196. The smallest perfect square greater than 197 is 225. Find the square
and root of each number:
So,
. Write an inequality. Simplify.
is between 14 and 15. Since 197 is much closer to 196 than 225, the best whole number estimate for is 14.
3. SOLUTION: The largest perfect square less than 15.6 is 9. The smallest perfect square greater than 15.6 is 16. Find the square
root of each number:
So,
and . Write an inequality. Simplify.
is between 3 and 4. Since 15.6 is much closer to 16 than 9, the best whole number estimate for is 4.
4. SOLUTION: The largest perfect square less than 85.1 is 81. The smallest perfect square greater than 85.1 is 100. Find the square
root of each number:
and . Write an inequality. Simplify.
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So,
is between 9 and 10. Since 85.1 is closer to 81 than 100, the best whole number estimate for Page 1
is 9.
1-9 Estimate Roots
So,
is between 3 and 4. Since 15.6 is much closer to 16 than 9, the best whole number estimate for is 4.
4. SOLUTION: The largest perfect square less than 85.1 is 81. The smallest perfect square greater than 85.1 is 100. Find the square
root of each number:
So,
and . Write an inequality. Simplify.
is between 9 and 10. Since 85.1 is closer to 81 than 100, the best whole number estimate for is 9.
5. SOLUTION: The largest perfect cube less than 22 is 8. The smallest perfect cube greater than 22 is 27. Find the cube root of each
number:
. Write an inequality. Simplify.
and So,
is between 2 and 3. Since 22 is closer to 27 than 8, the best whole number estimate for
is 3.
6. SOLUTION: The largest perfect cube less than 34 is 27. The smallest perfect cube greater than 34 is 64. Find the cube root of
each number:
. Write an inequality. Simplify.
and So,
is between 3 and 4. Since 34 is closer to 27 than 64, the best whole number estimate for
is 3.
7. SOLUTION: The largest perfect cube less than 989 is 729. The smallest perfect cube greater than 989 is 1,000. Find the cube root
of each number:
. Write an inequality. Simplify.
and So,
is between 9 and 10. Since 989 is closer to 1,000 than 729, the best whole number estimate for eSolutions Manual - Powered by Cognero
8. SOLUTION: is 10.
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1-9 Estimate Roots
So,
is between 3 and 4. Since 34 is closer to 27 than 64, the best whole number estimate for
is 3.
7. SOLUTION: The largest perfect cube less than 989 is 729. The smallest perfect cube greater than 989 is 1,000. Find the cube root
of each number:
. Write an inequality. Simplify.
and So,
is between 9 and 10. Since 989 is closer to 1,000 than 729, the best whole number estimate for is 10.
8. SOLUTION: The largest perfect cube less than 250 is 216. The smallest perfect cube greater than 250 is 343. Find the cube root of
each number:
. Write an inequality. Simplify.
and So,
is between 6 and 7. Since 250 is closer to 216 than 343, the best whole number estimate for eSolutions Manual - Powered by Cognero
is 6.
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