Roots as Inverse Growth Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Estimate \(\sqrt{50}\) to one decimal place by finding the two perfect squares it lies between.

Solution

  1. 1
    Find perfect squares near 50: \(7^2 = 49\) and \(8^2 = 64\).
  2. 2
    So \(7 < \sqrt{50} < 8\).
  3. 3
    Since 50 is very close to 49: \(\sqrt{50} \approx 7.1\).
  4. 4
    Check: \(7.1^2 = 50.41 \approx 50\). ✓

Answer

\(\sqrt{50} \approx 7.1\)
Estimate square roots by bracketing between consecutive perfect squares, then narrowing down. \(\sqrt{50} \approx 7.07\).

About Roots as Inverse Growth

Roots reverse the process of exponentiation: the nnth root of aa finds the number that, raised to the nnth power, produces aa. For example, 83=2\sqrt[3]{8} = 2 because 23=82^3 = 8.

Learn more about Roots as Inverse Growth →

More Roots as Inverse Growth Examples

Example 1 easy

Since (8^2 = 64), what is (sqrt{64})? Explain roots as inverses of powers.

Example 3 easy

Find (sqrt{144}) and (sqrt[3]{27}).

Example 4 medium

Between which two consecutive integers does (sqrt{75}) lie? Estimate to one decimal.

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