Find the real number whose square is equal to the difference between the square of 37 and the square of 23. Give your answer correct to two decimal places.

Introduction / Context:

This question checks your ability to work with squares of numbers and to interpret the phrase whose square is equal to a given value. It is essentially asking for the positive square root of a difference of two squares, a pattern that appears often in basic algebra and quantitative aptitude.

Given Data / Assumptions:

• We are given the numbers 37 and 23.
• We need to compute 37^2 - 23^2.
• The required number is the positive real number whose square equals this difference.
• The final answer must be reported correct to two decimal places.

Concept / Approach:

First, calculate 37^2 and 23^2 directly. Then subtract the smaller square from the larger to get the difference. Finally, take the positive square root of that difference. You can use the identity a^2 - b^2 = (a + b)(a - b) to simplify the arithmetic if you like.

Step-by-Step Solution:

Verification / Alternative check:

You can check by squaring 28.98: 28.98 * 28.98 is approximately 839.84, which is very close to 840. Small rounding differences are expected because we rounded to two decimal places.

Why Other Options Are Wrong:

Values like 45.09 or 47.09 give squares much larger than 840. The value 28 (without decimals) has a square equal to 784, which is significantly lower than 840. The value 32.50 has a square above 1000, which is not correct. Only 28.98 is consistent with the required square value when rounding is considered.

Common Pitfalls:

A common mistake is to subtract 23 from 37 first and then square the result, computing (37 - 23)^2 instead of 37^2 - 23^2. Another error is rounding too early or with insufficient precision, leading to a noticeably incorrect squared value.

Final Answer:

The required number, correct to two decimal places, is 28.98.