Question

What is the square root of 400 ?

Short answer

The square root of 400 is 20.

Step-by-step solution

Understand the Problem

We need to find the square root of 400. This means we are looking for a number which, when multiplied by itself, results in 400.

Identify Perfect Squares

Start by identifying perfect squares that are near 400. We know that 20 squared is 400 because: \[ 20 \times 20 = 400 \]

Verify the Solution

Check whether squaring the identified number (20) gives back 400: \[ 20^2 = 400 \] This confirms that the square root of 400 is indeed 20.

Key concepts

Perfect Squares

Perfect squares are numbers that can be expressed as the product of an integer with itself. Understanding perfect squares is a key component in dealing with square roots. Essentially, if you know the basics of multiplying numbers, you are already familiar with the concept of perfect squares.

Here are some common perfect squares to remember:

• 1, since \(1 \times 1 = 1\)
• 4, since \(2 \times 2 = 4\)
• 9, since \(3 \times 3 = 9\)
• 16, since \(4 \times 4 = 16\)
• 25, since \(5 \times 5 = 25\)

Recognizing patterns in numbers helps when solving problems. For instance, if you are aware that 20 squared equals 400, it simplifies finding the square root of 400. Knowing perfect squares broadens your number sense, which is crucial in math problem solving.

Mathematical Operations

To solve mathematical problems like finding square roots, understanding basic operations is essential. Multiplication is a fundamental operation used when determining the square of a number.

Imagine multiplication as repeated addition. To find the square of 4, for example, you calculate \(4 \times 4\), which results in 16. Similarly, \(20 \times 20\) results in 400, as demonstrated in finding the square root of 400.

In mathematics, there are two symbols you often see: the square \( ^2 \) and the square root \( \sqrt{} \). The square of a number is simply that number times itself, and the square root operation is the inverse, meaning if \( n^2 = x \), then \( \sqrt{x} = n \). Using these operations, math becomes a system of finding relationships between numbers.

Problem Solving

Problem solving in mathematics often involves a series of logical steps. It's like a detective solving a mystery, where you use clues (or math concepts) to find the answer. Here’s a simple three-step approach:

• **Understand the Problem**: Clearly define what is being asked. In this case, "Find the square root of 400."
• **Identify Known Information**: Determine relevant facts you know. Knowing the perfect square closest to your target number, here 400, is helpful. We know from our understanding of perfect squares that 20 squared equals 400.
• **Verify the Solution**: After calculating, always check your work. Multiply 20 by itself to confirm it equals 400; this step ensures that your answer is correct.

This systematic approach enhances accuracy and efficiency. More importantly, developing problem-solving skills helps in tackling various mathematical challenges with confidence.