What approximate value will come in place of ‘x’ in the following equation?

$39.99\%\text{of}299.98+\sqrt{168.96}=x^2+51.97$

The correct answer is 16.

Step-by-step explanation:

We are given the following equation to approximate:

$39.99\%\text{of}299.98+\sqrt{168.96}=x^2+51.97$

Step 1: Round each decimal value to its nearest whole number for approximation:

• $39.99\%\approx 40\%$

• $299.98\approx 300$

• $\sqrt{168.96}\approx \sqrt{169}=13$

• $51.97\approx 52$

Step 2: Calculate the simplified values on the left-hand side (LHS):

$40\%\text{of}300=\frac{40}{100}\times 300=120$

Add the square root term:

$\text{LHS}=120+13=133$

Step 3: Solve for x:

Substituting the simplified values into the equation:

$133=x^2-123$

$x^2=133+123$

$x^2=256$

$x=\sqrt{256}$

$x=16$

Hence, the approximate value of x is 16.