square root of -45?

(using imaginary numbers)

http://www.google.com/search?q=sqrt+-45&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

Calculate square root without a calculator
Explanation of three ways to find square roots without calculator, including the Babylonian method.
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
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Math Forum: Ask Dr. Math FAQ: Square and Cube Roots
How do you find the square root of a number without a calculator? ... Start with the number you want to find the square root of. Let's use 12. ...
http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html
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Square Root Calculator
The Square Root Calculator will find the square root of the number you enter. ... Related Topic How to calculate square roots without a calculator ...
http://www.math.com/students/calculators/source/square-root.htm
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How to manually find a square root
The way to do find a square root without a calculator.
http://math.arizona.edu/~kerl/doc/square-root.html
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How to Find the Square Root of a Number
Learn how to find the square root of a number without using a calculator.
http://www.math-videos-online.com/find-the-square-root-of-a-number.html

by definition i = √-1

so √-45 = √-1 x √9 x √5
= 3i√5

To find the square root of a negative number, we need to use imaginary numbers. The square root of a negative number is represented by the imaginary unit, denoted as "i." The imaginary unit is defined as the square root of -1.

To find the square root of -45 using imaginary numbers, we can follow these steps:

Step 1: Express -45 as the product of a positive number and -1.
-45 = 45 * -1

Step 2: Take the square root of the positive number.
√45

Step 3: Express the square root of -1 using the imaginary unit, i.
√(-1) = i

Step 4: Combine the results from step 2 and step 3.
√45 * i

Therefore, the square root of -45 is √45i.