Comparison Math Example 4

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

Example 4

medium
Without a calculator, determine which is larger: 50\sqrt{50} or 7.17.1.

Solution

  1. 1
    Square both values to compare: 502=50\sqrt{50}^2 = 50 and 7.12=50.417.1^2 = 50.41.
  2. 2
    Since 50<50.4150 < 50.41 and the square function is increasing for positive numbers, 50<7.1\sqrt{50} < 7.1.

Answer

50<7.1\sqrt{50} < 7.1
When comparing a square root to a decimal, squaring both sides preserves the inequality (since both are positive). This avoids estimating the irrational value and gives an exact comparison.

About Comparison

Determining how two quantities relate in terms of size or value, using the symbols <<, >>, or ==.

Learn more about Comparison →

More Comparison Examples

Example 1 easy

Compare [formula] and [formula]. Which is greater?

Example 2 medium

Place [formula], [formula], [formula], and [formula] in order from least to greatest.

Example 3 easy

Insert [formula], [formula], or [formula] between each pair: (a) [formula] and [formula], (b) [formu

← All Comparison Examples Comparison Concept