Math Problem Statement

Calculate \( \sqrt{(1.7)^2} \).

Solution

The given expression is:

(1.7)2.\sqrt{(1.7)^2}.

Step-by-step Solution:

  1. Simplify the square inside the square root: (1.7)2=1.7×1.7=2.89.(1.7)^2 = 1.7 \times 1.7 = 2.89.

  2. Take the square root of 2.892.89: 2.89=1.7.\sqrt{2.89} = 1.7.

Thus, the solution is:

1.7.1.7.


Would you like further explanation or examples? Here are five related questions to explore this concept further:

  1. What happens if the square root includes a negative number, such as (1.7)2\sqrt{(-1.7)^2}?
  2. Can the square root operation be applied to cube roots in a similar way?
  3. How is the square root function related to the power of 12\frac{1}{2}?
  4. Why does (x)2=x\sqrt{(x)^2} = |x| instead of xx in general?
  5. How can this calculation be applied in real-world scenarios, such as physics or geometry?

Tip:

Whenever you simplify expressions involving x2\sqrt{x^2}, always remember that the square root of a square gives the absolute value of the base.

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Math Problem Analysis

Mathematical Concepts

Square roots
Exponents
Simplifying expressions

Formulas

\( \sqrt{x^2} = |x| \)

Theorems

Properties of square roots and exponents

Suitable Grade Level

Grades 6-8