Question

Simplify each expression. \(\sqrt{121}\)

Short answer

The simplified expression is 11.

Step-by-step solution

Identify the Expression

The expression we need to simplify is \( \sqrt{121} \), which represents the square root of 121.

Recognize Perfect Squares

Recall that finding the square root involves identifying a number that, when multiplied by itself, equals the given number. Recognize that 121 is a perfect square because 11 multiplied by 11 equals 121.

Calculate the Square Root

Since 11 times 11 gives us 121, the square root of 121 is therefore 11. Thus, \( \sqrt{121} = 11 \).

Key concepts

Perfect Squares

Understanding perfect squares is key when simplifying square roots. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 1, 4, 9, 16, and 25 are all perfect squares. This is because:

• 1 = 1 × 1
• 4 = 2 × 2
• 9 = 3 × 3
• 16 = 4 × 4
• 25 = 5 × 5

Recognizing perfect squares quickly helps us simplify square roots more efficiently. If you know that 121 is a perfect square, you directly find its square root without extra steps.

Square Root Calculation

The square root calculation involves finding a number which, when squared (multiplied by itself), equals the given number. In the problem at hand, we're dealing with \(\sqrt{121}\).

This symbol \(\sqrt{}\) is called a radical, and the number inside the radical is known as the radicand. Calculating \(\sqrt{121}\) comes down to determining which number multiplied by itself will yield 121. In this case, this number is 11, because \(11 \times 11 = 121\).

Therefore, \(\sqrt{121} = 11\).

Calculating square roots is easier when the radicand is a perfect square, making recognition of perfect squares essential for quicker resolution.

Mathematical Expressions

In mathematics, expressions are combinations of numbers, symbols, and operators (like addition, subtraction, multiplication, and division) that represent a value. The expression in our example is a simplified form involving a square root: \(\sqrt{121}\).

Expressions can vary in complexity. They can be simple like \(\sqrt{121}\) or complex involving multiple terms and operators. Simplification is a process used to make expressions easier to work with by removing any unnecessary parts or by breaking them down into their simplest form. When simplifying square root expressions, the goal is often to reduce them to a basic integer value, if possible.

In the case of \(\sqrt{121}\), it results in the integer 11, fulfilling the criteria of simplifying a mathematical expression.