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Chapter 10: Problem 2

Solve the given equation. $$\sqrt{y}=10$$

Short Answer

Expert verified
y = 100

Step by step solution

01

Understand the equation

The given equation is \(\sqrt{y}=10\). To solve for \(y\), we need to eliminate the square root.
02

Square both sides of the equation

To get rid of the square root, square both sides of the equation: \(\sqrt{y}^2 = 10^2\), which simplifies to \(y = 100\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

square roots
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16: \(4 \times 4 = 16\). The symbol for the square root is \(\sqrt{}\). In the given equation, \(\sqrt{y}=10\), we need to find out what number \(y\) is, whose square root equals 10. This means we are looking for a number that when multiplied by itself gives 100, because 10 \(\times\) 10 equals 100. Square roots are very common in math and often appear in various types of equations.
squaring both sides
To solve equations involving square roots, one often uses a technique called 'squaring both sides'. This means you raise both sides of the equation to the power of 2 to eliminate the square root. In our example, the equation is \(\sqrt{y}=10\). To remove the square root, you can square both sides: \( (\sqrt{y})^2 = 10^2 \). Squaring the square root, \(\sqrt{y}\), cancels out the square root, leaving just \(y\). So, \( (\sqrt{y})^2 \ = y \) and \( 10^2 = 100 \). Therefore, squaring both sides yields \( y = 100 \). This technique is very useful for simplifying and solving equations with square roots.
elementary algebra
Elementary algebra involves basic algebraic operations and concepts that are fundamental in solving equations. These include understanding variables, constants, operations, and the principles of equality and inverse operations. In our solved example, we see these principles in action. We start with the equation \(\sqrt{y}=10\), and use an inverse operation (squaring) to isolate the variable \(y\). In doing so, elementary algebra helps us transform and solve the equation. It's all about breaking down complex problems into simpler steps using basic algebraic rules. Mastering these fundamental concepts is key to tackling more advanced math topics in the future.

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Most popular questions from this chapter

Perform the indicated operations and simplify. $$\frac{y^{2}+2 y}{y^{2}-4} \div \frac{y^{2}}{y^{2}-6 y+8}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{28}-\sqrt{7}$$

Factor the given expression as completely as possible. $$x^{2}-6 x-7$$

Sketch the graph of each equation in a rectangular coordinate system. Label the intercepts. $$5 y-2 x=10$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{12}+\sqrt{27}$$
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