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Chapter 11: Problem 2

With the help of a calculator find (a) \(\sqrt{7}\), (b) \(\sqrt{-7}\), (c) \(\sqrt{5.32}\), (d) \(\sqrt{-5.32}\)

Short Answer

Expert verified
Answer: (a) The square root of 7 is approximately 2.65. (b) The square root of -7 is approximately 2.65i. (c) The square root of 5.32 is approximately 2.31. (d) The square root of -5.32 is approximately 2.31i.

Step by step solution

01

Understanding Square Roots

To find the square root of a number, you are looking for a value that, when multiplied by itself, will give you the original number. Using a calculator, you can usually find the square root by entering the number and pressing the "√" button.
02

Identifying Real and Complex Solutions

When the number under the square root is positive, you can find a real solution. However, when the number is negative, there is no real number that can be multiplied by itself to give a negative result. In this case, the answer will be a complex solution involving the imaginary unit "i", where i² = -1.
03

Solving (a) \(\sqrt{7}\)

To find the square root of 7, use the calculator to enter the number 7 and press the "√" button. The result will be a real number: \(\sqrt{7} \approx 2.65.\)
04

Solving (b) \(\sqrt{-7}\)

Since -7 is negative, the square root will not have a real solution. Instead, we can rewrite it as a complex number: \(\sqrt{-7} = \sqrt{7i^2}\). The answer will be a multiple of the imaginary unit "i": \(\sqrt{-7} \approx 2.65i\).
05

Solving (c) \(\sqrt{5.32}\)

To find the square root of 5.32, use the calculator to enter the number 5.32 and press the "√" button. The result will be a real number: \(\sqrt{5.32} \approx 2.31.\)
06

Solving (d) \(\sqrt{-5.32}\)

Since -5.32 is negative, it will have a complex solution. Rewrite it as a complex number: \(\sqrt{-5.32} = \sqrt{5.32i^2}\). The answer will be a multiple of the imaginary unit "i": \(\sqrt{-5.32} \approx 2.31i\). Now you have the square roots of the given numbers: (a) \(\sqrt{7} \approx 2.65\), (b) \(\sqrt{-7} \approx 2.65i\), (c) \(\sqrt{5.32} \approx 2.31\), and (d) \(\sqrt{-5.32} \approx 2.31i\).

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