Calculating the Square Root

Oct 13, 2025 by thesweetdesigns.com 56 views

Solving the Equation: $h^2 = 0.36$

Understanding the Problem

When solving an equation, it's essential to consider all possible solutions. In this case, we're given the equation $h^2 = 0.36$ , and we need to determine which values of $h$ satisfy this equation. We'll explore each option and provide a detailed explanation of the solution process.

Option A: $h = \sqrt{0.36}$

To solve for $h$ , we can take the square root of both sides of the equation. This gives us:

$h = \sqrt{0.36}$

Since the square root of a number is the value that, when multiplied by itself, gives the original number, we can simplify this expression by finding the square root of 0.36.

Calculating the Square Root

To calculate the square root of 0.36, we can use a calculator or perform the calculation manually. The square root of 0.36 is approximately 0.6.

h = √0.36 ≈ 0.6

Therefore, option A is a valid solution to the equation $h^2 = 0.36$ .

Option B: $h = -\sqrt{0.36}$

Now, let's consider option B, which states that $h = -\sqrt{0.36}$ . To evaluate this option, we need to understand the concept of negative square roots.

Negative Square Roots

When we take the square root of a number, we can get both a positive and a negative result. For example, the square root of 16 is both 4 and -4, since both 4^2 and (-4)^2 equal 16.

√16 = ±4

In the case of option B, we're considering the negative square root of 0.36. Since the square root of 0.36 is approximately 0.6, the negative square root would be:

h = -√0.36 ≈ -0.6

Therefore, option B is also a valid solution to the equation $h^2 = 0.36$ .

Option C: $h = 0.18$

Now, let's examine option C, which states that $h = 0.18$ . To determine if this is a valid solution, we can substitute 0.18 into the original equation and see if it holds true.

h^2 = 0.18^2 = 0.0324

As we can see, 0.18^2 does not equal 0.36. Therefore, option C is not a valid solution to the equation $h^2 = 0.36$ .

Conclusion

In conclusion, the solutions to the equation $h^2 = 0.36$ are:

$h = \sqrt{0.36} ≈ 0.6$
$h = -\sqrt{0.36} ≈ -0.6$

These two values satisfy the equation, while option C, $h = 0.18$ , does not.

Key Takeaways

When solving an equation, it's essential to consider all possible solutions.
The square root of a number can be both positive and negative.
To determine if a value is a solution to an equation, substitute it into the equation and see if it holds true.

Additional Resources

For more information on solving equations and working with square roots, check out the following resources:

Khan Academy: Solving Equations
Mathway: Square Root Calculator
Wolfram Alpha: Square Root Function
Frequently Asked Questions: Solving the Equation $h^2 = 0.36$

Q: What is the equation $h^2 = 0.36$ trying to solve for?

A: The equation $h^2 = 0.36$ is trying to solve for the value of $h$ . We're looking for a value of $h$ that, when squared, equals 0.36.

Q: How do I solve for $h$ in the equation $h^2 = 0.36$ ?

A: To solve for $h$ , we can take the square root of both sides of the equation. This gives us:

$h = \sqrt{0.36}$

Q: What is the square root of 0.36?

A: The square root of 0.36 is approximately 0.6.

Q: Are there any other solutions to the equation $h^2 = 0.36$ ?

A: Yes, there is another solution to the equation $h^2 = 0.36$ . In addition to $h = \sqrt{0.36}$ , we also have:

$h = -\sqrt{0.36}$

This is because the square root of a number can be both positive and negative.

Q: Why is $h = 0.18$ not a solution to the equation $h^2 = 0.36$ ?

A: $h = 0.18$ is not a solution to the equation $h^2 = 0.36$ because when we square 0.18, we get:

$0.18^2 = 0.0324$

This does not equal 0.36, so $h = 0.18$ is not a valid solution.

Q: What is the difference between a positive and negative square root?

A: The positive square root of a number is the value that, when multiplied by itself, gives the original number. The negative square root of a number is the value that, when multiplied by itself, gives the original number, but with a negative sign.

Q: How do I know which solution to choose?

A: When solving an equation, it's essential to consider all possible solutions. In this case, we have two solutions: $h = \sqrt{0.36}$ and $h = -\sqrt{0.36}$ . Both of these values satisfy the equation, so we can choose either one as a solution.

Q: What if I have a different equation to solve? How do I know which solution to choose?

A: When solving a different equation, you'll need to follow the same steps as before: take the square root of both sides of the equation and consider all possible solutions. If you're unsure which solution to choose, you can always substitute the values back into the original equation to see which one works.

Q: Are there any online resources that can help me solve equations like $h^2 = 0.36$ ?

A: Yes, there are many online resources available to help you solve equations like $h^2 = 0.36$ . Some popular resources include:

Khan Academy: Solving Equations
Mathway: Square Root Calculator
Wolfram Alpha: Square Root Function

These resources can provide you with step-by-step instructions and examples to help you solve equations like $h^2 = 0.36$ .

Q: Can I use a calculator to solve equations like $h^2 = 0.36$ ?

A: Yes, you can use a calculator to solve equations like $h^2 = 0.36$ . In fact, calculators can be a great tool for solving equations quickly and accurately. However, it's always a good idea to double-check your work by plugging the values back into the original equation.