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Chapter 0: Problem 115

Solve each equation, rounding your answer to four significant digits where necessary. $$ x^{1 / 2}-4=0 $$

Short Answer

Expert verified
The solution to the equation \(x^{1/2} - 4 = 0\) is \(x = 16\).

Step by step solution

01

Add 4 to both sides of the equation

To isolate the square root term, we will add 4 to both sides of the equation to get rid of the subtraction of 4: \(x^{1/2} - 4 + 4 = 0 + 4\)
02

Simplify the equation

Simplify the equation to have: \(x^{1/2} = 4\)
03

Square both sides of the equation

To get rid of the square root, we will square both sides of the equation: \((x^{1/2})^2 = 4^2\)
04

Simplify and solve for x

Simplify the equation and solve for x: \(x = 16\)
05

Check the solution

Verify that the solution is correct by substituting the value of x back into the original equation: \((16)^{1/2} - 4 = 0\) \(4 - 4 = 0\) \(0 = 0\) The solution is correct. The value of x is 16, and there is no need to round as it is an exact whole number.

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Most popular questions from this chapter

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(-x^{2}-2 x-1=0\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(\frac{\left(\frac{2}{3}\right)}{5}\)

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(\frac{12-(1-4)}{2(5-1) \cdot 2-1}\)

Calculate each expression in Exencises giving the answer as \(a\) whole mumber or a fraction in lowest terms.\(1-3 \cdot(-2)^{2} \times 2\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3\left(1+\frac{4}{100}\right)^{-3}\)
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