Square Roots: Complete the missing numbers

To solve this problem, we will perform the following steps:

• Step 1: Square both sides of the equation $\sqrt{x} = 6$.
• Step 2: Simplify the equation to find $x$.

Let's carry out each step in detail:

Step 1: Square both sides of the equation:
$\ (\sqrt{x})^2 = 6^2$

Step 2: Simplify the equation:
Since $(\sqrt{x})^2 = x$, we have $x = 36$.

Therefore, the value of $x$ is 36.

To solve the problem, follow these steps:

• Step 1: Begin with the equation $\sqrt{x} = 2$.
• Step 2: Square both sides of the equation to eliminate the square root.
• Step 3: Simplify the resulting equation to find $x$.

Now, let's proceed through each step:
Step 1: The given equation is $\sqrt{x} = 2$.
Step 2: Square both sides: $(\sqrt{x})^2 = 2^2$.
Step 3: This simplifies to $x = 4$.

Therefore, the value of $x$ that satisfies $\sqrt{x} = 2$ is $x = 4$.

Matching this solution with the provided choices, the correct answer is choice 3, which is 4.

To solve this problem, we'll follow these steps:

• Step 1: Square both sides of the equation.
• Step 2: Simplify the resulting expression.

Now, let's work through each step:

Step 1: We have the equation $\sqrt{x} = 1$.
Square both sides:

$(\sqrt{x})^2 = 1^2$

Step 2: Simplify both sides of the equation.

The left side simplifies to $x$, since the square and the square root cancel each other out:

$x = 1$

The right side simplifies to 1, so we have:

$x = 1$

Therefore, the solution to the problem is $x = 1$.

To solve the problem $\sqrt{☐} = 8$, we follow these steps:

• Step 1: Identify the equation given, which is $\sqrt{☐} = 8$.

• Step 2: To solve for $☐$, we need to eliminate the square root. We do this by squaring both sides of the equation:

  $(\sqrt{☐})^2 = 8^2$

• Step 3: Simplify both sides:

  On the left, $(\sqrt{☐})^2$ simplifies to $☐$, and on the right, $8^2 = 64$.

• Step 4: This gives us the equation $☐ = 64$.

Thus, the value of $☐$ is 64.

Therefore, the solution to the problem is $64$.

To solve this problem, we will eliminate the square root by squaring both sides of the equation.

• Step 1: Start with the given equation:
  $\sqrt{x} = 7$
• Step 2: Square both sides of the equation to eliminate the square root:
  $(\sqrt{x})^2 = 7^2$
• Step 3: Simplify both sides:
  $x = 49$
• This calculation shows that when the square root of $x$ is 7, the value of $x$ must be 49 to satisfy the equation.

Therefore, the solution to the problem is $x = 49$. This matches the correct choice from the given multiple-choice options.

To solve the equation $\sqrt{x} = 12$, we need to eliminate the square root by squaring both sides.

Let's follow these steps:

• Step 1: Square both sides of the equation to remove the square root:

$(\sqrt{x})^2 = 12^2$

• Step 2: Simplify the squared terms:

$x = 144$

Therefore, the value of $x$ that satisfies the equation is $\boxed{144}$.

Confirming with the choices given, the correct answer is 144, which matches choice 2.

To solve the given problem, we will follow these steps:

• Step 1: Square both sides of the equation
• Step 2: Simplify to find $x$

Now, let's work through each step:

Step 1: We are given $\sqrt{x} = 15$.
To eliminate the square root, square both sides of the equation:

$(\sqrt{x})^2 = 15^2$

Step 2: Simplify both sides:
On the left, $(\sqrt{x})^2 = x$.
On the right, $15^2 = 225$.

This gives us the equation:

$x = 225$

Thus, the solution to the problem is $\boxed{225}$.

To solve this problem, we'll follow the steps below:

• Step 1: Start with the given equation: $\sqrt{x} = 14$.
• Step 2: Square both sides of the equation to eliminate the square root:

$(\sqrt{x})^2 = 14^2$

Step 3: Calculate the square of 14:
$14 \times 14 = 196$

Therefore, the value of $x$ is 196.

Comparing our solution with the provided choices, choice 3 ($196$) is the correct match.

Thus, the solution to the problem is $x = 196$.

To solve this problem, we'll follow these steps:

• Step 1: Simplify the given power.
• Step 2: Set up the equation using what we know about square roots.
• Step 3: Solve for $x$ using appropriate calculations.

Now, let's work through each step:
Step 1: Simplify $2^2$. We calculate $2^2 = 4$.
Step 2: Set up the equation: $\sqrt{x} = 4$.
Step 3: Square both sides to solve for $x$.
$x = 4^2 = 16$

Therefore, $\boxed{16}$ is the solution to the problem, which matches with choice 2.

To solve this problem, follow these steps:

• Step 1: Begin with the given equation:

$\sqrt{x} = 20$

• Step 2: Square both sides of the equation to eliminate the square root. When you square a square root, you are left with the number inside the square root:

$(\sqrt{x})^2 = 20^2$

• Step 3: Simplify both sides of the equation:

$x = 400$

Therefore, the solution to the problem is $x = 400$.

The correct choice from the provided options is 400.