Solving a Number Equation Involving Its Square Root: A Guide for SEOers

SEOers are often required to understand and solve mathematical problems to optimize content and improve search engine rankings. One common type of problem involves finding a number based on its product with its square root. This article will guide you through solving the problem: 'If the product of a number and its square root is 8, what is the number?'

Understanding the Problem

Consider a number x. The problem states that the product of the number and its square root is 8. Mathematically, this can be represented as:

x √x 8

Step-by-Step Solution

Step 1: Define the Equation

Starting with the equation x √x 8, our goal is to find the value of x. Here’s how we can approach it:

Step 2: Isolate the Square Root

First, we isolate the square root term:

√x 8 / x

Step 3: Eliminate the Square Root

Next, we square both sides to eliminate the square root:

(√x)2 (8 / x)2

x (8 / √x)2

Step 4: Simplify the Equation

When we simplify the equation:

x (82) / x

x 64 / x

Multiplying both sides by x (assuming x ≠ 0) yields:

x2 64

Step 5: Solve for x

Finally, we take the square root of both sides:

x plusmn;√64

x 8 or -8

However, the square root of a negative number is not defined in the real number system. Therefore, we discard -8, leaving us with:

x 8

Algebraic Solutions Using Different Techniques

Alternatively, the problem can be approached differently:

Direct Solution

Express the problem as:

x3 64

Since 64 is 43, we find:

x 4

The equation can also be solved by recognizing that:

xfrac32; 8 implies x3 82 64 x 4