Write a Java expression for the following:

$$\frac{\sqrt{3x+x^2}}{a+b}$$

Math.sqrt(3 * x + x * x) / (a + b)

Practice with a program

Here's a simple Java program that calculates the given mathematical expression:

<span class="pln">
</span><span class="kwd">public</span><span class="pln"> </span><span class="kwd">class</span><span class="pln"> </span><span class="typ">MathExpression</span><span class="pln"> </span><span class="pun">{</span><span class="pln">
    </span><span class="kwd">public</span><span class="pln"> </span><span class="kwd">static</span><span class="pln"> </span><span class="kwd">void</span><span class="pln"> main</span><span class="pun">(</span><span class="typ">String</span><span class="pun">[]</span><span class="pln"> args</span><span class="pun">)</span><span class="pln"> </span><span class="pun">{</span><span class="pln">
        </span><span class="com">// Define values for x, a, and b</span><span class="pln">
        </span><span class="kwd">double</span><span class="pln"> x </span><span class="pun">=</span><span class="pln"> </span><span class="lit">5</span><span class="pun">;</span><span class="pln"> </span><span class="com">// Example value for x</span><span class="pln">
        </span><span class="kwd">double</span><span class="pln"> a </span><span class="pun">=</span><span class="pln"> </span><span class="lit">2</span><span class="pun">;</span><span class="pln"> </span><span class="com">// Example value for a</span><span class="pln">
        </span><span class="kwd">double</span><span class="pln"> b </span><span class="pun">=</span><span class="pln"> </span><span class="lit">3</span><span class="pun">;</span><span class="pln"> </span><span class="com">// Example value for b</span><span class="pln">

        </span><span class="com">// Calculate the expression: Math.sqrt(3 * x + x * x) / (a + b)</span><span class="pln">
        </span><span class="kwd">double</span><span class="pln"> result </span><span class="pun">=</span><span class="pln"> </span><span class="typ">Math</span><span class="pun">.</span><span class="pln">sqrt</span><span class="pun">(</span><span class="lit">3</span><span class="pln"> </span><span class="pun">*</span><span class="pln"> x </span><span class="pun">+</span><span class="pln"> x </span><span class="pun">*</span><span class="pln"> x</span><span class="pun">)</span><span class="pln"> </span><span class="pun">/</span><span class="pln"> </span><span class="pun">(</span><span class="pln">a </span><span class="pun">+</span><span class="pln"> b</span><span class="pun">);</span><span class="pln">

        </span><span class="com">// Display the result</span><span class="pln">
        </span><span class="typ">System</span><span class="pun">.</span><span class="kwd">out</span><span class="pun">.</span><span class="pln">println</span><span class="pun">(</span><span class="str">"Result: "</span><span class="pln"> </span><span class="pun">+</span><span class="pln"> result</span><span class="pun">);</span><span class="pln">
    </span><span class="pun">}</span><span class="pln">
</span><span class="pun">}</span><span class="pln">
</span>

Explanation:

• 3 * x + x * x computes the numerator inside the square root.
• Math.sqrt(...) takes the square root of that numerator.
• The denominator is (a + b).
• The final result is obtained by dividing the square root value by (a + b).

You can modify the values of x, a, and b to test different cases. 🚀