How To Find The Square Root of a Negative Number

TL;DR

When simplifying square root expressions with negative numbers, introduce imaginary numbers. The square root of negative 9 is 3i.

Transcript

how would you simplify this expression what is the square root of negative 9. how can we find the square root of a negative number let's compare this to the square root of 9. the square root of 9 is 3 because we know that 3 times 3 is equal to 9. but now if we were to multiply negative 3 together that will also give us positive 9. we can't find two... Read More

Key Insights

• ❎ When simplifying square root expressions with negative numbers, introduce imaginary numbers.
• ❎ The square root of a negative number can be expressed as the square root of the positive value times the square root of negative one.
• ❎ In simplifying square root expressions with negative numbers, identify the highest perfect square that goes into the given number.
• ❎ Imaginary numbers allow us to find the square root of negative numbers and solve quadratic equations.
• ❎ When taking the square root of x squared, there are two possible answers: the positive and negative square root of x.

Questions & Answers

Q: How do we simplify the square root of a negative number?

When simplifying the square root of a negative number, we introduce imaginary numbers. We can break it down into the square root of the positive value times the square root of negative one, which is equal to i.

Q: What is the value of the square root of negative 9?

The square root of negative 9 is equal to 3i. We can break it down as the square root of 9 times the square root of negative one, resulting in 3i.

Q: How can we simplify the square root of negative 49?

The square root of negative 49 can be simplified as 7i. We can break it down as the square root of 49 times the square root of negative one, resulting in 7i.

Q: How do we simplify the square root of negative 75?

To simplify the square root of negative 75, we break it down into the highest perfect square that goes into it, which is 25. Therefore, it becomes 5√3i.

Summary & Key Takeaways

• When simplifying square root expressions with negative numbers, introduce imaginary numbers.

• The square root of negative 9 is equal to 3i.

• The highest perfect square that goes into a given number can be used to simplify square root expressions with negative numbers.