Problem 8 Solve each equation. $$ \sqr... [FREE SOLUTION]

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Chapter 10: Problem 8

Solve each equation. $$ \sqrt{x+1}=7 $$

Short Answer

Expert verified

x = 48

Step by step solution

Isolate the Square Root

The given equation is $\root{x+1}=7$. The square root is already isolated on one side of the equation.

Square Both Sides

To eliminate the square root, square both sides of the equation. This gives us: \[ (\root{x+1})^2 = 7^2 \] which simplifies to \[ x + 1 = 49 \]

Solve for x

Subtract 1 from both sides to solve for \x\: \[ x + 1 - 1 = 49 - 1 \] which simplifies to \[ x = 48 \]

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Key Concepts

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

isolate the square root

To solve square root equations, the first key step is to isolate the square root. In simpler terms, you need to make sure the square root is by itself on one side of the equation. For example, given the equation $\root[x+1]=7$, you can see the square root $\root[x+1]$ is already alone on the left side. If it weren't, you'd need to manipulate the equation until the square root is isolated. This might involve moving other terms to the opposite side of the equation using addition, subtraction, multiplication, or division. By isolating the square root, you make the next steps much more straightforward.

square both sides

Once the square root is isolated, the next step is to eliminate it. We do this by squaring both sides of the equation. Squaring effectively cancels out the square root. In our example, we start with $\root[x+1]=7$. Square both sides to get:
\[ (\root[x+1])^2 = 7^2 \]
This simplifies to:
\[ x + 1 = 49 \]
It's important to square correctly. Make sure to square the entire side, not just individual terms. Once you've squared both sides and simplified, you'll have a much simpler equation to solve.

solve for x

Now that the square root is gone, it's time for the final step: solving for x. With the simplified equation from the previous step, \[ x + 1 = 49 \], you can solve for x by isolating it. To do this, subtract 1 from both sides of the equation:
\[ x + 1 - 1 = 49 - 1 \]
This simplifies to:
\[ x = 48 \]
And there you have it! You've solved the equation and found that \[ x = 48 \]. Always remember to double-check your solution by plugging it back into the original equation to ensure it works. This way, you can be confident in your answer.

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91影视

Solve each equation. $$ \sqrt{x+1}=7 $$

Short Answer

Step by step solution

Isolate the Square Root

Square Both Sides

Solve for x

Key Concepts

isolate the square root

square both sides

solve for x

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