Solved on Mar 20, 2024

The given statement $\sqrt{-400}=20 i$ is false. The correct solution is $\sqrt{-400}=20i$ .

STEP 1

1. The square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ .
2. The square root of a negative number $-a$ is $i$ times the square root of the positive number $a$ .

STEP 2

1. Evaluate the square root of the positive part of the number.
2. Introduce the imaginary unit $i$ for the negative part.
3. Compare the result with the given statement and decide if it is true or false.
4. If false, provide the correct expression.

STEP 3

Evaluate the square root of the positive part of the number $400$ .
$\sqrt{400} = 20$

STEP 4

Introduce the imaginary unit $i$ to account for the negative sign in the original expression.
$\sqrt{-400} = \sqrt{400} \cdot \sqrt{-1} = 20 \cdot i$

STEP 5

Compare the result with the given statement.
The given statement is $\sqrt{-400} = 20i$ and the result from STEP_2 is also $20i$ .

STEP 6

Since the result matches the given statement, the statement is true.
$\sqrt{-400} = 20i$

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The given statement $\sqrt{-400}=20 i$ is false. The correct solution is $\sqrt{-400}=20i$ .

STEP 1

1. The square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ .
2. The square root of a negative number $-a$ is $i$ times the square root of the positive number $a$ .

STEP 2

1. Evaluate the square root of the positive part of the number.
2. Introduce the imaginary unit $i$ for the negative part.
3. Compare the result with the given statement and decide if it is true or false.
4. If false, provide the correct expression.

STEP 3

Evaluate the square root of the positive part of the number $400$ .
$\sqrt{400} = 20$

STEP 4

Introduce the imaginary unit $i$ to account for the negative sign in the original expression.
$\sqrt{-400} = \sqrt{400} \cdot \sqrt{-1} = 20 \cdot i$

STEP 5

Compare the result with the given statement.
The given statement is $\sqrt{-400} = 20i$ and the result from STEP_2 is also $20i$ .

STEP 6

Since the result matches the given statement, the statement is true.
$\sqrt{-400} = 20i$

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The given statement −400=20i\sqrt{-400}=20 i−400​=20i is false. The correct solution is −400=20i\sqrt{-400}=20i−400​=20i.

STEP 1

1. The square root of a negative number involves the imaginary unit iii, where i2=−1i^2 = -1i2=−1.2. The square root of a negative number −a-a−a is iii times the square root of the positive number aaa.

STEP 2

1. Evaluate the square root of the positive part of the number.2. Introduce the imaginary unit iii for the negative part.3. Compare the result with the given statement and decide if it is true or false.4. If false, provide the correct expression.

STEP 3

Evaluate the square root of the positive part of the number 400400400.400=20 \sqrt{400} = 20 400​=20

STEP 4

Introduce the imaginary unit iii to account for the negative sign in the original expression.−400=400⋅−1=20⋅i \sqrt{-400} = \sqrt{400} \cdot \sqrt{-1} = 20 \cdot i −400​=400​⋅−1​=20⋅i

STEP 5

Compare the result with the given statement.The given statement is −400=20i\sqrt{-400} = 20i−400​=20i and the result from STEP_2 is also 20i20i20i.

STEP 6

Since the result matches the given statement, the statement is true.−400=20i \sqrt{-400} = 20i −400​=20i

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The given statement $\sqrt{-400}=20 i$ is false. The correct solution is $\sqrt{-400}=20i$ .

1. The square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ .
2. The square root of a negative number $-a$ is $i$ times the square root of the positive number $a$ .

1. Evaluate the square root of the positive part of the number.
2. Introduce the imaginary unit $i$ for the negative part.
3. Compare the result with the given statement and decide if it is true or false.
4. If false, provide the correct expression.

Evaluate the square root of the positive part of the number $400$ .
$\sqrt{400} = 20$

Introduce the imaginary unit $i$ to account for the negative sign in the original expression.
$\sqrt{-400} = \sqrt{400} \cdot \sqrt{-1} = 20 \cdot i$

Compare the result with the given statement.
The given statement is $\sqrt{-400} = 20i$ and the result from STEP_2 is also $20i$ .

Since the result matches the given statement, the statement is true.
$\sqrt{-400} = 20i$